Question

Together, two boys had 43 cents. The first boy spent 5 cents and the second boy spent 13 cents. The first boy’s remaining money is 2/3
of the second boy’s remaining money. How much did they each have originally?

Answer 1

hello kiddio lets figure this out!

Let x = first 

y = second 

Then 

x - 5 = remainder of first 

y - 13 = remainder of second 

x - 5 = 2/3(y - 13) 

3x - 15 = 2y - 26 

3x - 2y = - 11................(1) 

x + y = 43....................(2) 

From (2) y = 43 - x..........(3) 

Put (3) in (1) 

3x - 2(43 - x) = - 11 

3x - 86 + 2x = - 11 

5x = 75 

x = 15 cents 

y = 43 - 15 

= 28 cents

Have  a nice day

Answer 2

The first boy has total 15 cents originally and the second boy has 28 cent originally before spending a single amount of money.

What is an unknown variable?

Unknown variables are used to find the unknown values of the problem using the algebraic expressions.

To find the values of unknown quantity, the statements of a problem is converted in the algebraic equation form using the variable in place of unknown numbers.

Let suppose the first boy has x cents ang the second boy has y cents. As together, these two boys had 43 cents. Therefore,

$x+y=43$

$y=43-x$             ....1

The first boy spent 5 cents and the second boy spent 13 cents. The first boy’s remaining money is 2/3 of the second boy’s remaining money.

$(x-5)=\dfrac{2}{3}(y-13)\\3x-15=2y-26$

Put the value of from equation one in the above equation as,

$3x-15=2(43-x)-26\\3x+2x=86-26+15\\5x=75\\x=\dfrac{75}{5}\\x=15$

Put this value in the equation one as,

$y=43-15\\y=28$

Hence, the first boy has total 15 cents originally and the second boy has 28 cent originally before spending a single amount of money.

Learn more about the unknown variable here;

https://brainly.com/question/1235185