Sarah is two-thirds as old as Jenny. Jenny is 7 years older than Sarah. Which system of equations could be used to find the girls’ ages?

A. 3s – 2j = 0
j – 7 = s

B. j = 2/3s
s + 7 = j

C. j – 2/3 = s
j – s = 7

D. 2/3j = s
j + 7 = s

and what is your thinking?

i think its D. is that right?

To solve this problem, let's assign variables to the girls' ages. Let's say Sarah's age is represented by "s" and Jenny's age is represented by "j".

From the given information, we know that Sarah is two-thirds as old as Jenny. This can be written as the equation:
s = (2/3)j

We are also told that Jenny is 7 years older than Sarah. This can be written as the equation:
j = s + 7

To find the system of equations that could be used to solve the girls' ages, we need to look for equations that match the relationships described above.

Let's go through the given options:
A. 3s – 2j = 0
j – 7 = s
These equations do not match the relationship described. The coefficients in the first equation (3 and 2) are not consistent with the given information. Eliminate option A.

B. j = (2/3)s
s + 7 = j
These equations match the given information. The first equation states that Jenny's age is two-thirds of Sarah's age, as described. The second equation states that Jenny is 7 years older than Sarah, as described. Retain option B.

C. j – (2/3) = s
j – s = 7
The first equation does not match the relationship described. The second equation states that Jenny and Sarah are 7 years apart, not that Jenny is 7 years older than Sarah. Eliminate option C.

D. (2/3)j = s
j + 7 = s
These equations do not match the relationship described. In the first equation, the coefficient is reversed compared to the given information. Eliminate option D.

Based on our analysis, the system of equations that could be used to find the girls' ages is:
j = (2/3)s
s + 7 = j

Therefore, the correct answer is option B.