4
algebra

A zoo has monkeys and parrots. There are 28 animals with 76 legs. How many monkeys are there? (Monkeys have 4 legs, parrots have 2 legs)

A

8 monkeys

B

10 monkeys

C

12 monkeys

D

14 monkeys

Correct Answer: B

Choice B is the correct answer. Let mm = monkeys and pp = parrots.

System: {m+p=284m+2p=76\begin{cases} m + p = 28 \\ 4m + 2p = 76 \end{cases}

Step 1: From first: p=28mp = 28 - m

Step 2: Substitute: 4m+2(28m)=764m + 2(28 - m) = 764m+562m=764m + 56 - 2m = 762m=202m = 20m=10m = 10

Solution: 10 monkeys

Verification: 10+18=2810 + 18 = 28 ✓ and 4(10)+2(18)=40+36=764(10) + 2(18) = 40 + 36 = 76

💡 Strategic Tip: Count heads for one equation, legs for the other.