Help with 5th grade homework PLEASE!!!

[jacksonsmom]

I am trying to help my son with his math homework, we are all stuck on one question. I am stuck on how to figure out the answer.
Can any one help????

Here is the question:

Benjamin went into the store and spent $16 more then half the money he had in his pocket. This left him with $16. How much money did he have in his pocket before he went into the store?


ANY help would be SO much appreciated. I guess I am NOT smarter than a 5th grader!

 

[abdmom]

I am trying to help my son with his math homework, we are all stuck on one question. I am stuck on how to figure out the answer.
Can any one help????

Here is the question:

Benjamin went into the store and spent $16 more then half the money he had in his pocket. This left him with $16. How much money did he have in his pocket before he went into the store?


ANY help would be SO much appreciated. I guess I am NOT smarter than a 5th grader!

Let the amount of money in his pocket before he went in = x

(1/2x + 16 ) (amount spent) +16(amount left after spending) = x (total)

32 = 1/2 x

64 = x

 

[Hoodie]

Let the amount of money in his pocket before he went in = x

(1/2x + 16 ) (amount spent) +16(amount left after spending) = x (total)

32 = 1/2 x

64 = x

This (you type faster! )

 

[jacksonsmom]

OK, I am still very confused.....trying to wrap my brain around it.

How did you get 32????

I am so lost, and want to explain it to him instead of just giving him the answer.

 

[Mickey'snewestfan]

While I agree with the algebra above, I don't think the teacher's expecting an algebraic solution. With a fifth grader I'd either guess and check until we got to the solution:

e.g. Well, let's make a guess, what if he had $100 in his pocket. He spent 1/2 (that's $50) and then he spent $16 more. How much would he have left? $32? Hmmm, that's too much, I bet $100 was too much too. What could we try next? $50? OK, let's try that . . . . That leaves us with $9. That's closer, but not right, so we need a number between $100 and $50, but closer to $50.

Or I'd step backwards. Let's pretend it's 2 steps. He spent 1/2 his money and then he spent $16. Now he has $16 left. How much did he have before he spent that last $16? He had $32. If he had money, and he spent 1/2 then what he spent must been equal to what he had left after he spent 1/2. So how much did he spend? 32. If he had $32 after he spent $32, how much did he have before . . .

 

[mjkacmom]

OP, I don't want to scare you, but by 6th grade, I could no longer help with math (BA in English, though). Fortunately, I have a DH who is great in math, and actually uses it every day for work. Find someone now, before it's too late. My DH already knows he's on call for other kids if they need help.

 

[NotUrsula]

I'm not good at math, either, but word problems involving money tend to have a solid $ answer, so they are straightforward.

"Benjamin went into the store and spent $16 more then half the money he had in his pocket. This left him with $16. How much money did he have in his pocket before he went into the store?"

As someone else pointed out, let X be the amount that he had in his pocket. (The rest of my notation is unorthodox, but I still get the correct answer.)

(X / 2) - 16 = 16

So if he has 16 now and he spent at least 16, that would mean that he started out with at least 32.

(X / 2) = 32

So, what number, divided by half, would give you 32? 64

 

[kellydizfan]

My DD's 16 & 13 guessed he had $48 dollars to start.

 

[jacksonsmom]

My DD's 16 & 13 guessed he had $48 dollars to start.

This was my first answer, but now everyone saying $64...I am even now more confused, although it I think I am slowly "getting it"

(I hate Math!)

 

[Tinkh]

Ok my son says it is 48 too. I am so a psych and biology girl, so I am not much help. Something about if statements lol. He is in Algebra II if that helps. I asked him to explain it to me so I could explain to you and he just gave me a look like I am crazy haha.

 

[Tinkh]

Ok, I see what they are seeing. Ugh. I hate that I can't stop thinking about this. I took a needed break from studying cardiopulmonary anatomy and physiology and stumbled into more thinking.

If you have 16 and spent 16. Then you had at least 32. Half of that is 16. So 32 plus 16 is 48.

 

[gonzo76]

My son is in Algebra and said "48"

Me...No clue

 

[Big Cuddly Bear]

My DD's 16 & 13 guessed he had $48 dollars to start.

That was what I thought.

 

[Big Cuddly Bear]

I am trying to help my son with his math homework, we are all stuck on one question. I am stuck on how to figure out the answer.
Can any one help????

Here is the question:

Benjamin went into the store and spent $16 more then half the money he had in his pocket. This left him with $16. How much money did he have in his pocket before he went into the store?


ANY help would be SO much appreciated. I guess I am NOT smarter than a 5th grader!

Ok, I think 64 now...

half of 64 is 32. He spent $16 more than "half" so add that to 32, and you get $48. Now add the $16 he still has to $48, and you get $64.

 

[MrsToad]

I always have to do each step; I hope I've got it.

Let T = total to start. Let S = spent.

We know that what he spent was $16 more than 1/2 the total, so:
S = 1/2 T + 16

Then, we know that after the purchase, he had $16 left, so:
T - S = 16

Then add S to both sides of the second equation to solve for T:
T - S + S = 16 + S which solves to T = 16 + S

Substitute 16 + S for T in the first equation:
S = 1/2(16 + S) + 16

Multiply everything by 2 to get rid of the fraction:
2S = (16 + S) + 32 which then becomes 2S = 16 + S + 32

This then simplies to 2S = 48 + S

Subtract S from both sides:
2S - S = 48 + S - S which becomes S = 48

HOWEVER, since S equals "Spent," you still need to solve for the "Total:"

Since we know that the Total less what was spent left him with $16, go back to:
T - S = 16

Since we know S = 48, substitue 48 for S:
T - 48 = 16

Add 48 to both sides to get:
T - 48 + 48 = 16 + 48 which resolves to T = 64

Benjamin started with $64.

 

[Big Cuddly Bear]

I always have to do each step; I hope I've got it.

Let T = total to start. Let S = spent.

We know that what he spent was $16 more than 1/2 the total, so:
S = 1/2 T + 16

Then, we know that after the purchase, he had $16 left, so:
T - S = 16

Then add S to both sides of the second equation to solve for T:
T - S + S = 16 + S which solves to T = 16 + S

Substitute 16 + S for T in the first equation:
S = 1/2(16 + S) + 16

Multiply everything by 2 to get rid of the fraction:
2S = (16 + S) + 32 which then becomes 2S = 16 + S + 32

This then simplies to 2S = 48 + S

Subtract S from both sides:
2S - S = 48 + S - S which becomes S = 48

HOWEVER, since S equals "Spent," you still need to solve for the "Total:"

Since we know that the Total less what was spent left him with $16, go back to:
T - S = 16

Since we know S = 48, substitue 48 for S:
T - 48 = 16

Add 48 to both sides to get:
T - 48 + 48 = 16 + 48 which resolves to T = 64

Benjamin started with $64.

My head just exploded. But as I posted above you, I agree... $64 is the answer.

 

[MrsToad]

My head just exploded. But as I posted above you, I agree... $64 is the answer.

I always seemed to use a lot of paper in math class .

 

[FayeW]

To simplify the explanation for your son, let's put it this way:

We know that he has $16 left, and that he spent $16 more than half of what he had. If he had not spent the extra $16, he would have spent exactly half his money. Adding the $16 he spent extra with the $16 he has left and you will give you half of what he started with, $32, so he must have had $64 to start with.

 

[NotUrsula]

Well, we can check it by reversing the sense of the answer. Start with what you THINK that he had at the beginning, and work backward to the $16 that we know he ended up with:

"Benjamin went into the store and spent $16 more then half the money he had in his pocket. This left him with $16. How much money did he have in his pocket before he went into the store?"

So, if he had $48 when he started and he spent $16 more than half of that, he would have spent: $40 (48 / 2 = 24. 24 + 16 = 40)

$48 - $40 is NOT equal to $16.

However, half of $64 is $32. Add $16 to $32 and you get a total EXPENDITURE of $48. (64 / 2 = 32. 32 + 16 = 48)
$64 - $48 = $16

If you answer $48 your calculations are valid, but you're giving a differerent answer than the one that is asked for. $48 is what he spent, not what he started out with in his pocket. This is why word problems bother a lot of people who otherwise are good at math; it seems that very often the answer that would seem to be the most logical thing to solve for in an algebraic sense is not the part of the solution that the problem is asking for. (Lucky me, I never could make sense of algebraic logic; I never could figure out what I was supposed to be looking for if the problem was just a bunch of numbers. Give me a story to go with it, though, and the answer always falls into place for me.)

 

[Tinkh]

Well, we can check it by reversing the sense of the answer. Start with what you THINK that he had at the beginning, and work backward to the $16 that we know he ended up with:

"Benjamin went into the store and spent $16 more then half the money he had in his pocket. This left him with $16. How much money did he have in his pocket before he went into the store?"

So, if he had $48 when he started and he spent $16 more than half of that, he would have spent: $40 (48 / 2 = 24. 24 + 16 = 40)

$48 - $40 is NOT equal to $16.

However, half of $64 is $32. Add $16 to $32 and you get a total EXPENDITURE of $48. (64 / 2 = 32. 32 + 16 = 48)
$64 - $48 = $16

If you answer $48 your calculations are valid, but you're giving a differerent answer than the one that is asked for. $48 is what he spent, not what he started out with in his pocket.

Well said and sort of how I finally figured out why my son said 48 lol. Good explanation!