So, to begin, we can set the scenario into an equation to solve for the amount of magnets that Sarah had...
Joseph had 28 magnets, plus an unknown amount, x :
28 + x
Sarah had 157, plus the same unknown amount.
157 + x
Also, Sarah had four times the amount of Joseph at the end:
4(28 + x)
As a full equation:
![157 + x = 4(28 + x)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/2nktwiwct1ew6z8wx1fzydhvvd9ymc462b.png)
Now, all we have to do is solve for x, the unknown amount:
![157 + x = 4(28 + x)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/2nktwiwct1ew6z8wx1fzydhvvd9ymc462b.png)
Use the Distributive Property on 4(28 + x):
![157 + x = 112 + 4x](https://img.qammunity.org/2019/formulas/mathematics/middle-school/y9q9b1bbyb3869jezwqpi2ek40qgihuhvy.png)
Subtract x on both sides:
![157 + x - x = 112 + 4x - x](https://img.qammunity.org/2019/formulas/mathematics/middle-school/zad8q4k9fxfaergu5dxb0gmlwup6pqt007.png)
![157 = 112 + 3x](https://img.qammunity.org/2019/formulas/mathematics/middle-school/g8kbyen12en4i9u9jglurjw9360cpw8pdj.png)
Subtract 112 on both sides:
![157 - 112 = 112 - 112 + 3x](https://img.qammunity.org/2019/formulas/mathematics/middle-school/76zi4ridh2fkdywlyridnokpphnmmzygty.png)
![45 = 3x](https://img.qammunity.org/2019/formulas/mathematics/middle-school/9sqdtejxlf0qjlpcisp2nch4v0bnw1e81y.png)
Divide by 3 on both sides:
![15 = x](https://img.qammunity.org/2019/formulas/mathematics/middle-school/2ovnz7edwzsp0wia97b0pc16nc4cs9giy9.png)
15 is the unknown amount added to each pile of magnets!
Hope I could help you out!
Have a good one, and God bless!