# Diana purchased 6 pounds of strawberries and 4 pounds of apples for $18.90. Then she realized that this was not enough and purchased 3 more pounds of each fruit for$10.74. What was the cost per pound for each type of fruit?

May 9, 2017

The strawberries cost $2.29 per pound and the apples cost$1.29 per pound.

#### Explanation:

Based on the question, we can assume that the cost per pound of each type of fruit is constant, meaning that the cost per pound of strawberries for the 6 pounds of strawberries is the same as the cost per pound of strawberries for the additional 3 pounds Diana bought after realizing she did not buy enough.

To solve this problem, we need to set up our system of equations:
Let $t$ be the cost per pound for strawberries and $a$ be the cost per pound of apples.
For both purchases, we can write the equations in word form:
(pounds of strawberries)(cost per pound of strawberries) + (pounds of apples)(cost per pound of apples) = (total cost of purchase)

For her initial purchase:
$6 t + 4 a = 18.9$
For the second purchase:
$3 t + 3 a = 10.74$

Using this system of equations of two equations and two variables, we can solve for $t$ and $a$. To use elimination, we first double the second equation:
$6 t + 6 a = 21.48$
Then subtract the first equation from this modified second equation:
$6 t + 6 a - \left(6 t + 4 a\right) = 21.48 - 18.9$
$6 t + 6 a - 6 t - 4 a = 2.58$
$2 a = 2.58$
$a = 1.29$

To find t, we can substitute this value of $a$ into $6 t + 4 a = 18.9$ and solve for $t$:
$6 t + 4 \left(1.29\right) = 18.9$
$6 t = 18.9 - 4 \left(1.29\right)$
$6 t = 13.74$
$t = 2.29$

Therefore, the strawberries cost $2.29 per pound and the apples cost$1.29 per pound.