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Sana's mother bought produce for Sunday dinner. She bought one more pound of peaches than pounds of tomatoes. She bought 3 times as many pounds of tomatoes as pounds of mushrooms. If peaches cost $6 per lb, tomatoes cost $3 per lb, and mushrooms cost $10 per lb, how many of each did Sana's mother buy for $80?

Respuesta :

Using a system of equations, it is found that Sana's mother bought 6.72 pounds of peaches, 5.72 pounds of tomatoes and 2.24 pounds of mushrooms for $80.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

  • Variable x: Number of pounds of peaches.
  • Variable y: Number of pounds of tomatoes.
  • Variable z: Number of pounds of mushrooms.

She bought one more pound of peaches than pounds of tomatoes, hence:

x = y + 1.

y = x - 1.

She bought 3 times as many pounds of tomatoes as pounds of mushrooms, hence:

x = 3z.

y = x - 1 = 3z - 1.

She spent a total of $80, hence considering the cost per pound of each product we have that:

6x + 3y + 10z = 80.

Considering the values of x and y as function of z and replacing in the equation, we have that:

6(3z) + 3(3z - 1) + 10z = 80

18z + 9z - 3 + 10z = 80.

37z = 83.

z = 83/37

z = 2.24.

Then:

x = 3z = 3 x 2.24 = 6.72.

y = x - 1 = 3z - 1 = 6.72 - 1 = 5.72.

Hence, she bought 6.72 pounds of peaches, 5.72 pounds of tomatoes and 2.24 pounds of mushrooms for $80.

More can be learned about a system of equations at https://brainly.com/question/24342899

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