Answer:
Josh had $18 and Carly had $8.
Step-by-step explanation:
Given:
Josh had $10 more than Carly.
Josh gave Carly half of his money, then Carly had more money than josh, so she gave Josh $4. Then they both had $13.
Question asked:
How much money did each person start?
Solution:
Let Carly start with money be ![x](https://tex.z-dn.net/?f=x)
Then, Josh start with = ![x+10](https://tex.z-dn.net/?f=x%2B10)
According to question:
For Josh : ![x+10](https://tex.z-dn.net/?f=x%2B10)
<h3><em><u>Josh gave Carly half of $10 and received $4 from Carly having $13 at last, so the equation will be:-</u></em></h3>
![x+10-\frac{1}{2} (x+10)+4=13\\\\ x+10-\frac{x}{2}-5 +4=13\\ \\ x-\frac{x}{2}+9=13\\\\ \frac{2x-x}{2} +9=13\\\\ \frac{x}{2} +9=13](https://tex.z-dn.net/?f=x%2B10-%5Cfrac%7B1%7D%7B2%7D%20%28x%2B10%29%2B4%3D13%5C%5C%5C%5C%20x%2B10-%5Cfrac%7Bx%7D%7B2%7D-5%20%2B4%3D13%5C%5C%20%5C%5C%20x-%5Cfrac%7Bx%7D%7B2%7D%2B9%3D13%5C%5C%5C%5C%20%5Cfrac%7B2x-x%7D%7B2%7D%20%2B9%3D13%5C%5C%5C%5C%20%5Cfrac%7Bx%7D%7B2%7D%20%2B9%3D13)
Subtracting both sides by 9,
![\frac{x}{2} =4\\](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%20%3D4%5C%5C)
Multiplying both sides by 2,
![x=8](https://tex.z-dn.net/?f=x%3D8)
Carly start with money be
= $8
Josh start with =
= 8 + 10 = $18
Therefore, at starting, Josh had $18 and Carly had $8.