Estelle is making 30 pounds of fruit salad from strawberries and blueberries. Strawberries cost $1.80 per pound, and blueberries cost $4.50 per pound. If Estelle wants the fruit salad to cost her $2.52 per pound, how many pounds of each berry should she use?

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15-01-2019
Mathematics

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Estelle is making 30 pounds of fruit salad from strawberries and blueberries. Strawberries cost $1.80 per pound, and blueberries cost $4.50 per pound. If Estelle wants the fruit salad to cost her $2.52 per pound, how many pounds of each berry should she use?

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ColinJacobus ColinJacobus · Answer 1 · 2019-01-24T07:29:38+01:00

Answer: The answer is 22 pounds of Strawberries and 8 pounds of blueberries.

Step-by-step explanation: Let, Estelle should 'x' pounds of Strawberries and 'y' pounds of Blueberries in the fruit salad. Then according to the question, we have

[tex]x+y=30.[/tex]

Also, Strawberries cost $1.80per pound and Blueberries cost $4.50per pound, so we can write

[tex]1.80x+4.50y=30\times 2.52\\\\\Rightarrow \dfrac{9}{5}x+\dfrac{9}{2}y=\dfrac{3\times 126}{5}\\\\\Rightarrow \dfrac{1}{5}x+\dfrac{1}{2}y=\dfrac{42}{5}\\\\\Rightarrow \dfrac{2x+5y}{10}=\dfrac{42}{5}\\\\\Rightarrow 2x+5y=84.[/tex]

From the first equation, we get

[tex]2x+2y=60.[/tex]

Therefore, taking the difference of the above two equations, we have

[tex]5y-2y=84-60\\\\\Rightarrow 3y=24\\\\\Rightarrow y=8,[/tex]

and

[tex]x=30-8=22.[/tex]

Thus, Estelle should use 22 pounds of Strawberries and 8 pounds of Blueberries in the fruit salad.