How Much Money Did Frank Initially Have for School Supplies?

[S.R]

Homework Statement

Frank bought supplies for school. In the first store, he spent half his money plus $10. In the second store, he spent half of what he had left plus $10. In the third store, he spent 80% of what he had left. He came home with $5. How much did Frank start out with?

Homework Equations

The Attempt at a Solution

Any help would be appreciated.

Let x represent the original cost:

 

[mtayab1994]

I would say work in reverse start from the $5 and work your way back.

 

[Mark44]

Homework Statement

Frank bought supplies for school. In the first store, he spent half his money plus $10. In the second store, he spent half of what he had left plus $10. In the third store, he spent 80% of what he had left. He came home with $5. How much did Frank start out with?

Homework Equations

The Attempt at a Solution

Any help would be appreciated.

Let x represent the original cost:

Obviously, x = -35 is not the right answer.

Write a single equation that has on one side the amounts he spent in the three stores + what he had left, and on the other side, the total amount he started with (x).

 

[mtayab1994]

Obviously, x = -35 is not the right answer.

Write a single equation that has on one side the amounts he spent in the three stores + what he had left, and on the other side, the total amount he started with (x).

Or just do the inverse of what he spent starting out from $5.

 

[cesaruelas]

The problem is your second equation... the problem reads, he spent half of what he had left and what you wrote would mean he spent half of what he spent in the first store. You made the same mistake when writing the last one, the problem reads 80% of what he had left and you wrote 80% of what he spent. Try rewriting those and work the solution again.

 

[S.R]

Obviously, x = -35 is not the right answer.

Write a single equation that has on one side the amounts he spent in the three stores + what he had left, and on the other side, the total amount he started with (x).

Thanks for the advice. I know -35 is incorrect, that's why I posted the problem.

 

[cesaruelas]

Also, the assumption that S₃ is equal to 5 is wrong, that's what was left, not wht he spent in the third store (which is what you should write in S₃.

 

[S.R]

Also, the assumption that S₃ is equal to 5 is wrong, that's what was left, not wht he spent in the third store (which is what you should write in S₃.

Is S₂: [((x-(x/2+10))/2]-10?

 

[cesaruelas]

Is S₂: [((x-(x/2+10))/2]-10?

I would only change the last element and make it a + 10, the rest is okay according to me.

 

[S.R]

I would only change the last element and make it a + 10, the rest is okay according to me.

By "plus $10" does this mean Frank spends an additional $10 or that he spends one half plus $10?

 

[Mark44]

In the first store, he spent half his money plus $10

If he starts off with x dollars, the above can be translated to x/2 + 10, the amount he spent in the first store.

 

[S.R]

If he starts off with x dollars, the above can be translated to x/2 + 10, the amount he spent in the first store.

Yes. In the second store he spends (x-a)/2+10, where a=x/2+10. Correct? I'm still unclear on how to solve this problem.

 

[Mark44]

Looks good to me.

In store 1 he spent x/2 + 10, so he has left x - (x/2 + 10), or x/2 - 10.

In store 2 he spent half of what remained, plus $10.

Maybe it would help to make a table, listing how much he had when he went into each store, and how much when he came out.

 

[S.R]

Looks good to me.

In store 1 he spent x/2 + 10, so he has left x - (x/2 + 10), or x/2 - 10.

In store 2 he spent half of what remained, plus $10.

Maybe it would help to make a table, listing how much he had when he went into each store, and how much when he came out.

Store 1: he spent x/2+10, so he has left x/2-10.

Store 2: he spent [(x/2-10)/2]+10 = x/4+5, so he has left (x/2-10)-(x/4+5) = x/4-15.

Store 3: he spent 4/5*[x/4-15] = x/5-12, so he has left (x/4-15)-(x/5-12) = x/20-3.

Is this correct?

 

[Mark44]

Store 1: he spent x/2+10, so he has left x/2-10.

Store 2: he spent [(x/2-10)/2]+10 = x/4+5, so he has left (x/2-10)-(x/4+5) = x/4-15.

Store 3: he spent 4/5*[x/4-15] = x/5-12, so he has left (x/4-15)-(x/5-12) = x/20-3.

Is this correct?

Continue doing what you're doing until you get an equation that you can solve for x. Once you have a value, check it.

 

[S.R]

Continue doing what you're doing until you get an equation that you can solve for x. Once you have a value, check it.

Nevermind: answer is 160.