Question

Three times Toni's age added to twice Sam's age is 88 years. How old is Toni?

a) Toni is 32 years old.
b) Toni is 24 years old.
c) Toni is 40 years old.
d) Toni is 48 years old.
Sam's age reduced by half of Toni's age is 16 years. How old is Sam?
a) Sam is 24 years old.
b) Sam is 16 years old.
c) Sam is 20 years old.
d) Sam is 32 years old.

Answer 1

To find Toni's age, we use the equation 3T + 2S = 88 and isolate T. For Sam's age, we use the equation S - (1/2)T = 16 and substitute the expression for T from the first equation.

Step-by-step explanation:

To solve the first part of the question, let's use algebra. Let Toni's age be represented by 'T' and Sam's age be represented by 'S'. According to the given information, we can write the equation 3T + 2S = 88. Now, to find Toni's age, we need to isolate T. Subtract 2S from both sides of the equation to get 3T = 88 - 2S. Divide both sides by 3 to get T = (88 - 2S) / 3.

For the second part of the question, we can use another algebraic equation. Let's say Sam's age is 'S' and Toni's age is 'T'. We are given the equation S - (1/2)T = 16. Rearranging the equation, we have S = 16 + (1/2)T. Substitute the expression for T from the first equation into the second equation to get S = 16 + (1/2)((88 - 2S) / 3). Simplify this equation to find the value of S.