Question

Joaquin is four more than half Marjorie's age. Marjorie is also 32 less than three times Joaquin's age. How old is Marjorie?

a) 24 years old
b) 28 years old
c) 40 years old
d) 54 years old

Answer 1

Marjorie is 40 years old.

Step-by-step explanation:

To solve this problem, we need to set up an algebraic equation based on the information given. Let's define Marjorie's age as M and Joaquin's age as J:

J = (1/2)M + 4

M = 3J - 32

To find Marjorie's age, we can substitute the first equation into the second equation:

M = 3((1/2)M + 4) - 32

M = (3/2)M + 12 - 32

M = (3/2)M - 20

Subtracting (3/2)M from both sides gives:

(1/2)M = -20

M = -40

Since age cannot be negative, we get rid of the negative sign by taking the absolute value:

M = |-40| = 40

Therefore, Marjorie is 40 years old. The correct answer is (c) 40 years old.