Question

Tia owns a fruit shop and is selling a fresh lot of apples and oranges. She wants the ratio of apples to oranges sold to be 4 to 2. Tia

wants to sell a total of 54 apples and oranges. How many apples should she sell?
A.
52 apples
B. 36 apples
C. 9 apples
D. 32 apples

Answer 1

`\large \boxed{\text{B. 36 apples}}`

Explanation:

Let a = the number of apples

and o = the number of oranges

You have two conditions:

`\begin{array}{lrcl}(1) & (a)/(o) & = & (4)/(2) \\\\(2) & a+ o & = & 54\\\end{array}`

Solve the equations for a

`\begin{array}{rcll}2a & = & 4o & \text{Multiplied each side of (1) by 2o}\\\(3) \,2a - 4o& = & 0 &\text{Subtracted 4o from each side}\\a + o & = & 54& \text{This is equation (2)}\\(4) \, 4a +4o& = &216&\text{Multiplied each side by 4} \\6a& = &216&\text{Added (3) and (4)} \\a & = &\mathbf{36}&\text{Divided each side by 6} \\\end{array}\\\text{Tia should sell $\large \boxed{\textbf{36 apples}}$}`