Question

Help!!!

Answer 1

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:

$3x + 5y + z = 20$

$z = 20 - 3x - 5y$

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

This means that:

$3x + 2y + 2z = 21$

$3x + 2y + 2(20 - 3x - 5y) = 21$

$3x + 2y + 40 - 6x - 10y = 21$

$3x + 8y = 19$

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

This means that:

$4x + 3y + 3z = 30$

$4x + 3y + 3(20 - 3x - 5y) = 30$

$4x + 3y + 60 - 9x - 15y = 30$

$5x + 12y = 30$

For x and y, the system is:

$3x + 8y = 19$

$5x + 12y = 30$

Multiplying by 5 and -3, we get:

$15x + 40y = 95$

$-15x - 36y = -90$

Then, adding them:

$4y = 5$

$y = \frac{5}{4}$

$y = 1.25$

Each pound of grape cost $1.25.

Solving for x:

$5x + 12y = 30$

$5x + 12(1.25) = 30$

$5x = 15$

$x = \frac{15}{5}$

$x = 3$

Each pound of strawberry cost $3.

Finally, for z:

$z = 20 - 3x - 5y$

$z = 20 - 3(3) - 5(1.25)$

$z = 4.75$

Each pound of melon costs $4.75.

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