Sofia has 1,200 in savings and adds 35 each week. Mateo has... | SAT Systems of two linear equations in two variables Question, Answer Explained

Question bank / Systems of two linear equations in two variables

Math · AlgebraMedium

Sofia has $\$1{,}200$ in savings and adds $\$35$ each week. Mateo has $\$2{,}000$ in savings and adds $\$15$ each week. The equations $y = 1{,}200 + 35x$ and $y = 2{,}000 + 15x$ model their savings, $y$ dollars, after $x$ weeks. The solution to this system is $(40, 2{,}600)$ . What is the best interpretation of this solution?

A

After $40$ weeks, Sofia and Mateo will each have $\$2{,}600$ in savings.

B

After $40$ weeks, Sofia and Mateo will have a combined total of $\$2{,}600$ in savings.

C

After $2{,}600$ weeks, Sofia and Mateo will each have $\$40$ in savings.

D

After $2{,}600$ weeks, Sofia will have $\$40$ more in savings than Mateo.

Show answer and explanation

Answer: A

In the solution $(40, 2{,}600)$ , $x = 40$ weeks and $y = 2{,}600$ dollars, and the point lies on both lines. So after $40$ weeks each person has $\$2{,}600$ : $1{,}200 + 35(40) = 2{,}600$ and $2{,}000 + 15(40) = 2{,}600$ .

Choice B adds their savings, but each equation gives one person's savings, and the solution is where those two amounts are equal.

Why the other choices are wrong

B. Each equation models one person's savings. At the solution each person has $2,600, so together they have $5,200.
C. This switches the variables. x is the number of weeks, 40, and y is the amount saved, $2,600.
D. This switches the variables, and the solution is where the two amounts are equal, not where they differ.

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