SAT problem of the week, August 18, 2014 Solution

Hint for process of elimination: If we read carefully, we notice that the price of a single pair of shoes at the shoe store is \$latex a &s=1\$. The problem asks for the difference involving the cost of eight pairs of shoes at the shoe store. Therefore, the answer must have a term of \$latex 8a &s=1\$. This eliminates choices A, C, and E.

You can now try to reason through choices B and D. Since you eliminated three choices, you are statistically likely to improve your score by not leaving the answer blank, so you have to choose either B or D.

Read on for a full solution.

Solution: Let’s look more closely at one of the the sentences given:

…the eight pairs of shoes bought wholesale cost \$latex c &s=1\$ dollars less than eight pairs of shoes bought at the shoe store…

This is a word equation:

(the cost of eight pairs of shoes bought wholesale) [is] (\$latex c &s=1\$ dollars [less than]) (eight pairs of shoes bought at the shoe store)

The keyword “is” means “equals”, and the keyword “less than” means subtract at the end:

\$latex b=8a-c &s=1\$

Subtract \$latex b &s=1\$ from both sides to get

\$latex 8a-b-c=0 &s=1\$