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4. Three neighbors make a fruit salad for a summer picnic. One person uses three pounds of
strawberries, five pounds of grapes, and one pound of melon at a cost of $20. A second person uses
three pounds of strawberries, two pounds of grapes, and two pounds of melon at a cost of $21. The
last neighbor uses four pounds of strawberries, three pounds of grapes, and three pounds of melon
at a cost of $30. How much does each fruit cost?

Help 4 Three neighbors make a fruit salad for a summer picnic One person uses three pounds of strawberries five pounds of grapes and one pound of melon at a cos class=

Respuesta :

Using a system of equations, it is found that:

  • Each pound of strawberry cost $3.
  • Each pound of grape cost $1.25.
  • Each pound of melon costs $4.75.

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For our system, we have that:

  • x is the cost of a pound of strawberry.
  • y is the cost of a pound of grape.
  • z is the cost of a pound of melon.

Three pounds of  strawberries, five pounds of grapes, and one pound of melon at a cost of $20.

This means that:

[tex]3x + 5y + z = 20[/tex]

[tex]z = 20 - 3x - 5y[/tex]

Three pounds of strawberries, two pounds of grapes, and two pounds of melon at a cost of $21.

This means that:

[tex]3x + 2y + 2z = 21[/tex]

[tex]3x + 2y + 2(20 - 3x - 5y) = 21[/tex]

[tex]3x + 2y + 40 - 6x - 10y = 21[/tex]

[tex]3x + 8y = 19[/tex]

Four pounds of strawberries, three pounds of grapes, and three pounds of melon  at a cost of $30.

This means that:

[tex]4x + 3y + 3z = 30[/tex]

[tex]4x + 3y + 3(20 - 3x - 5y) = 30[/tex]

[tex]4x + 3y + 60 - 9x - 15y = 30[/tex]

[tex]5x + 12y = 30[/tex]

For x and y, the system is:

[tex]3x + 8y = 19[/tex]

[tex]5x + 12y = 30[/tex]

Multiplying by 5 and -3, we get:

[tex]15x + 40y = 95[/tex]

[tex]-15x - 36y = -90[/tex]

Then, adding them:

[tex]4y = 5[/tex]

[tex]y = \frac{5}{4}[/tex]

[tex]y = 1.25[/tex]

Each pound of grape cost $1.25.

Solving for x:

[tex]5x + 12y = 30[/tex]

[tex]5x + 12(1.25) = 30[/tex]

[tex]5x = 15[/tex]

[tex]x = \frac{15}{5}[/tex]

[tex]x = 3[/tex]

Each pound of strawberry cost $3.

Finally, for z:

[tex]z = 20 - 3x - 5y[/tex]

[tex]z = 20 - 3(3) - 5(1.25)[/tex]

[tex]z = 4.75[/tex]

Each pound of melon costs $4.75.

A similar problem is given at https://brainly.com/question/17096268

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