7
algebra

Anna is 3 times as old as her daughter. The sum of their ages is 48. How old is Anna?

A

30 years old

B

33 years old

C

36 years old

D

39 years old

Correct Answer: C

Choice C is the correct answer. Let AA = Anna's age and DD = daughter's age.

System: {A=3DA+D=48\begin{cases} A = 3D \\ A + D = 48 \end{cases}

Step 1: Substitute: 3D+D=483D + D = 484D=484D = 48D=12D = 12

Step 2: Find A: A=3(12)=36A = 3(12) = 36

Solution: Anna is 36 years old

Verification: 36+12=4836 + 12 = 48 ✓ and 36=3(12)36 = 3(12)

💡 Strategic Tip: "Times as old" translates to multiplication.