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?

Question

Genesis Allen · Accepted Answer

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

The question leads us to believe that the price per pound of each variety of fruit is constant, so the price per pound of strawberries for the six pounds Diana purchased and the three more pounds she purchased after realizing she had not purchased enough are equal. The first step in solving this problem is to set up our system of equations. For both purchases, we can write the equations in word form as follows: (pounds of strawberries)(cost per pound of strawberries) + (pounds of apples)(cost per pound of apples) = (total cost of purchase) For her initial purchase: #6t+4a=18.9# For the second purchase: #3t+3a=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: #6t+6a=21.48# Then subtract the first equation from this modified second equation: #6t+6a-(6t+4a)=21.48-18.9# #6t+6a-6t-4a=2.58# #2a=2.58# #a=1.29# To find t, we can substitute this value of #a# into #6t+4a=18.9# and solve for #t#: #6t+4(1.29)=18.9# #6t=18.9-4(1.29)# #6t=13.74# #t=2.29# Therefore, the strawberries cost $2.29 per pound and the apples cost $1.29 per pound.

Eva Abramson · Answer

undefined To find the cost per pound for each type of fruit, we can set up a system of equations. Let $ x $ be the cost per pound of strawberries and $ y $ be the cost per pound of apples.

From the first purchase:
$$ 6x + 4y = 18.90 $$

From the second purchase:
$$ 3x + 3y = 10.74 $$

Now, we can solve this system of equations to find the values of $ x $ and $ y $. First, let's simplify the second equation by dividing both sides by 3:
$$ x + y = 3.58 $$

Now, we can use the first equation to solve for one of the variables. Let's solve for $ x $:
$$ 6x + 4y = 18.90 $$
$$ 6x = 18.90 - 4y $$
$$ 6x = 18.90 - 4(3.58 - x) $$
$$ 6x = 18.90 - 14.32 + 4x $$
$$ 2x = 4.58 $$
$$ x = 2.29 $$

Now that we have found the value of $ x $, we can substitute it back into the second equation to find the value of $ y $:
$$ 2.29 + y = 3.58 $$
$$ y = 3.58 - 2.29 $$
$$ y = 1.29 $$

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