Question

Three times Allie's age plus twelve is equal to Sonya's age. Two times Allie's age plus four times Sonya's age is 188. How old is Sonya?

Option A: 24
Option B: 36
Option C: 42
Option D: 60

Answer 1

To solve the problem, set up a system of equations using Allie's age as A and Sonya's age as S. Solve the system of equations using substitution method, and find that Sonya is 42 years old.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's let Allie's age be represented by A and Sonya's age be represented by S. From the given information, we can write two equations:

Equation 1: 3A + 12 = S

Equation 2: 2A + 4S = 188

To solve this system of equations, we can use the method of substitution. We solve Equation 1 for S:

S = 3A + 12

Now, we substitute this expression for S in Equation 2:

2A + 4(3A + 12) = 188

Simplify and solve for A:

2A + 12A + 48 = 188

14A + 48 = 188

14A = 140

A = 10

Now, substitute this value of A into Equation 1 to find S:

S = 3(10) + 12

S = 42

So, Sonya is 42 years old.