1
algebra

A fruit stand sells apples for $1.50 per pound and oranges for $2 per pound. A customer bought 12 pounds of fruit for $21. How many pounds of apples were purchased?

A

6 pounds

B

5 pounds

C

7 pounds

D

8 pounds

Correct Answer: A

Choice A is the correct answer. Let aa = pounds of apples and oo = pounds of oranges.

System: {a+o=121.5a+2o=21\begin{cases} a + o = 12 \\ 1.5a + 2o = 21 \end{cases}

Step 1: From first: o=12ao = 12 - a

Step 2: Substitute: 1.5a+2(12a)=211.5a + 2(12 - a) = 211.5a+242a=211.5a + 24 - 2a = 210.5a=3-0.5a = -3a=6a = 6

Solution: 6 pounds of apples

Verification: 6+6=126 + 6 = 12 ✓ and 1.5(6)+2(6)=9+12=211.5(6) + 2(6) = 9 + 12 = 21

💡 Strategic Tip: Decimal coefficients can be eliminated by multiplying, but substitution works fine too.

**Other choices fail verification.