Darcy is buying apples and oranges for a large fruit basket to give away as a door prize at a charity event. apples cost $.24 each and oranges cost $.80 each. she has $12 to spend and would like to purchase at least 20 pieces of fruit total

Let x be the number of apples
Let y be the number of oranges

x+y≤20
0.24x+0.8y≤12

x≤20-y

0.24(20-y)+0.8y≤12
4.8-0.24y+0.8y≤12
0.56y≤7.2
y=12.9 (you can choose 12 here, since you can't have a fraction of an orange sold)

x= 7.14 (again, rounding this off to 7)

Therefore, Darcy got 12 oranges and 7 apples.

Hope I helped :)

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Abdulazeez10 Abdulazeez10 · Answer 2 · 2021-09-30T14:13:08+02:00

The system of linear inequalities that represent the situation are

$0.24x + $0.80y ≤ $12 and x + y ≥ 20

Here is the complete question:

Write a system of linear inequalities to represent this situation.

Darcy is buying apples and oranges for a large fruit basket to give away as a door prize at a charity event. Apples cost $0.24 each and oranges cost $0.80 each. She has $12 to spend and would like to purchase at least 20 pieces of fruit total.

To write a system of linear inequalities to represent the situation, we will consider the statements one after the other.

Let x represent the number of apples and y represent the number of oranges.

From the second statement,

"Apples cost $0.24 each and oranges cost $0.80 each"; and

From the next statement,

"She has $12 to spend"

That means, she can either spend $12 or less than $12.

Therefore, we can write that

$0.24x + $0.80y ≤ $12

Also, from the following statement

"and would like to purchase at least 20 pieces of fruit total"

That means, she will either purchase 20 pieces of fruit or greater than 20 pieces of fruit.

Then we can write that

x + y ≥ 20

Hence, the system of linear inequalities that represent the situation are

$0.24x + $0.80y ≤ $12 and x + y ≥ 20

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