Question

the cost of 12 oranges and 7 apples is $5.36. eight oranges and 5 apples cost $3.68. find the cost of each. (select 2))

Explanation:

Step1: Define variables for costs

Let $x$ = cost of 1 orange (in dollars), $y$ = cost of 1 apple (in dollars)

Step2: Set up system of equations

$$\begin{cases} 12x + 7y = 5.36 \\ 8x + 5y = 3.68 \end{cases}$$

Step3: Eliminate $x$ (scale equations)

Multiply first eq by 2: $24x + 14y = 10.72$
Multiply second eq by 3: $24x + 15y = 11.04$

Step4: Subtract equations to solve for $y$

$(24x + 15y) - (24x + 14y) = 11.04 - 10.72$
$y = 0.32$

Step5: Substitute $y$ to find $x$

Substitute $y=0.32$ into $8x + 5y = 3.68$:
$8x + 5(0.32) = 3.68$
$8x + 1.6 = 3.68$
$8x = 3.68 - 1.6 = 2.08$
$x = \frac{2.08}{8} = 0.26$

Answer:

Cost of one orange: $\$0.26$, Cost of one apple: $\$0.32$