Q 89 - Intermediate Algebra

Question

Nancy bought seven pounds of oranges and three pounds of bananas for $\backslash (17$. Her husband later bought three pounds of oranges and six pounds of bananas for $\backslash )12$. What was the cost per pound of the oranges and the bananas?

Step-by-Step Solution

Answer

The cost of oranges per pound is $\$2$ and the cost of bananas per pound is $\$1$

Step 1. Given

The cost of $7$ pounds of oranges and $3$ pounds of bananas is $\$17$

The cost of $3$ pounds of oranges and $6$ pounds of bananas is $\$12$

Step 2. Form linear equations

Let $x$ denote the cost of oranges per pound.

And $y$ denote the cost of bananas per pound.

The cost of $7$ pounds of oranges and $3$ pounds of bananas is $\$17$.

So, $7x+3y=17$

The cost of $3$ pounds of oranges and $6$ pounds of bananas is $\$12$.

So, $3x+6y=12$

Step 3. Solve the linear equations

So the linear equations are,

$7x+3y=17$

$3x+6y=12$

Divide the second equation by $3$,

   $x+2y=4$

          $x=4-2y$

Step 4. Solve for y

  Substitute $x=4-2y$ in the first equation,

          $7x+3y=17$

$7(4-2y)+3y=17$

$28-14y+3y=17$

        $28-11y=17$

          So, $11y=11$

Divide both sides of the equation by $11$,

                     $y=1$

The cost per pound of bananas is $\$1$

Step 5. Solve for x

Substitute $y=1$ in the equation,

          $x+2y=4$

       $x+2\left(1\right)=4$

                 $x=4-2$

                 $x=2$

The cost of ornages per pound is $\$2$

Step 6. Check the answer

Substitute $x=2$,

                  $y=1$ in the first equation,

        $7x+3y=\$17$

   $7\left(2\right)+3\left(1\right)=17$

          $14+3=17$

                $17=17$

Hence the equation holds true.