Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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 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=

Sagot :

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.

--------------------

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

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.