Mrs. Aiken bought some peaches at $1.49 per pound and some blueberries at $1.99 per pound to use in fruit salad she is making for an exciting math party at her house. She paid $20.38 for a total of 12 pounds of the two kinds of fruit. How many pounds of peaches did she buy?

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FRESHERTHANYOUU FRESHERTHANYOUU

03-03-2017
Mathematics

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Mrs. Aiken bought some peaches at $1.49 per pound and some blueberries at $1.99 per pound to use in fruit salad she is making for an exciting math party at her house. She paid $20.38 for a total of 12 pounds of the two kinds of fruit. How many pounds of peaches did she buy?

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rarrininger rarrininger · Answer 1 · 2017-03-03T03:09:58+01:00

P= peaches B=Blueberries
$1.49 p + $1.99 b = $20.38
p + b = 12 lbs.
Take p + b = 12 subtract p from both sides. b= 12-p
Now substitute b = 12 -p for b in $1.49 p + $1.99 b = $20.38
Looks like this $1.49 p + $1.99 ( 12-p ) = $20.38
Distribute $1.99 * 12 = 23.88
Distribute $1.99 * p = $1.99p
$1.49 p + $23.88 - $1.99p =$20.38
Combine $1.49 p - $1.99p = -0.50
-$0.50p + $23.88 = $20.38
Subtract $23.88 on both sides.
-$0.50p = -$3.50
Divide both sides by -$0.50
peaches= 7 lbs

psm22415 psm22415 · Answer 2 · 2022-01-21T18:40:48+01:00

She buys 7.2 pounds of peaches.

Given that

Mrs. Aiken bought some peaches at $1.49 per pound and some blueberries at $1.99 per pound to use in a fruit salad.

She is making for an exciting math party at her house.

She paid $20.38 for a total of 12 pounds of the two kinds of fruit.

We have to determine

How many pounds of peaches did she buy?

According to the question

Let the number of peaches be p,

And the number of blueberries be b.

Mrs. Aiken bought some peaches at $1.49 per pound and some blueberries at $1.99 per pound to use in a fruit salad.

[tex]\rm 1.49 p + 1.99 b = 20.38[/tex]

A total of 12 pounds of the two kinds of fruit.

[tex]\rm p + b = 12 [/tex]

On solving both the equation;

[tex]\rm 1.49 p + 1.99 b = 20.38\\ \\ p+b=12[/tex]

From equation 1,

[tex]\rm p+b=12\\ \\ p=12-b[/tex]

Substitute the value of p in equation 1,

[tex]\rm 1.49 (12-b) + 1.99 b = 20.38\\ \\ 17.98-1.49b+1.99b = 20.38\\ \\ 0.5b = 20.38-17.98\\ \\ 0.5b = 2.4\\ \\ b = \dfrac{2.4}{0.5}\\ \\ b = 4.8[/tex]

Substitute the value of b in equation 2

[tex]\rm p+b=12\\ \\ p = 12-b\\ \\ p = 12-4.8\\ \\ p = 7.2[/tex]

Hence, she buys 7.2 pounds of peaches.

To know more about the Equation click the link given below.

https://brainly.com/question/25806785