how many jelly beans did each girl have at first?

Question

Martha and Mary had $375$ jelly beans in all. After Mary ate $24$ jelly beans and Martha ate $\frac 17$ of her jelly beans, they each had the same number of jelly beans left. How many jelly beans did each girl have at first?

Answer 1

If Mary had $a$ and Martha had $b$ we have:

$a+b=375$

$a-24=\frac{6b}{7}$

Do you know how to solve these systems of equations?

Answer 2

Answer : Mary had $186$ jelly beans and Martha had $189$ jelly beans.

Explanation: If Mary had $x$ and Martha had $y$ :

$$x + y = 375\tag{1}$$

$$x − 24 = \frac{6y}{7} \tag{2}$$ If the value of $x $is replaced from $(1)$ into $(2)$, then $(2)$ will be,

$$375 - y - 24 = \frac{6y}{7}$$ $$\implies y(1+\frac67) = 375 - 24$$ $$\implies \frac{13}{7}y = 351$$ $$\implies y=\frac{351\cdot 7}{13} $$ $$\implies y = 189$$

Substitute the value of $y$ into $(1)$

$$\implies x = 375 - 189 = 186$$

To check if the solution is correct, both should have same number of jelly beans after Mary ate $24$ jelly beans and Martha ate $\frac{1}{7}^{th}$ portion of her jelly beans.

So,

$$x - 24 = 186 - 24 = 162$$ $$y - \frac y7 = 189 - \frac{189}7 = 189 - 27 = 162$$

So they both have same number of jelly beans after eating as stated hence the solution is correct.