Algebra - Set - 6 | SAT Math Section

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Mar 28, 2024

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Tom scored 85, 78, and 98 on his first three exams in history class. Solving which inequality gives the score, $G$, on Tom's fourth exam that will result in a mean score on all four exams of at least 90 ?

Difficulty: Easy

90-(85+78+98)\leq 4G

4G+85+78+98\geq 360

\dfrac{(G+85+78+98)}{4} \geq 90

\dfrac{(85+78+98)}{4}\geq 90-4G

In the system of equations below, $a$ and $c$ are constants.$$\frac{1}{2}x+\frac{1}{3}y=\frac{1}{6} \\ ax+y=c$$If the system of equations has an infinite number of solutions $(x,y)$, what is the value of $a$?

Difficulty: Hard

-\dfrac{1}{2}

$0$

\dfrac{1}{2}

-\dfrac{3}{2}

Sean rents a tent at a cost of $\$11$ per day plus a one-time insurance fee of $\$10$. Which equation represents the total cost $c$, in dollars, to rent the tent with insurance for $d$ days?

Difficulty: Easy

$c=11(d+10)$

$c=10(d+11)$

$c=11d+10$

$c=10d+11$

Keenan made 32 cups of vegetable broth. Keenan then filled $\bm{x}$ small jars and $\bm{y}$ large jars with all the vegetable broth he made. The equation $3\bm{x}+5\bm{y}=32$ represents this situation. Which is the best interpretation of $5\bm{y}$ in this context?

Difficulty: Hard

The number of large jars Keenan filled

The number of small jars Keenan filled

The total number of cups of vegetable broth in the large jars

The total number of cups of vegetable broth in the small jars

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