I need to solve "6 pounds of potatoes costs as much as 5 pounds of apples..."

[Nicole.ss]

Hello, I have two problems to solve and I didnt figure it out how to write good systems of equations for them. Here is the first problem.

8. Six pounds of potatoes costs as the same as five pounds of apples. In addition, three pounds of potatoes cost thirty cents more than two pounds of potatoes. How much (in dollars) would it cost to buy one pound of potatoes and one pound of apples?

Thank You,
Nicole

 

[MarkFL]

For the first problem, let A be the cost of a pound of apples and P be the cost of a pound of potatoes. How does the first sentence tell us to relate A and P?

 

[Nicole.ss]

It's like
6P = 5A
3P - 30 = 2A

and the answers I get is
P = -30/9
A = 30/13

Could you tell me what I do wrong?

 

[MarkFL]

Your equations are correct if you are using cents rather than dollars, which is fine.

Can you show the work you did that lead up to your incorrect solution?

 

[stapel]

8. Six pounds of potatoes costs as the same as five pounds of apples. In addition, three pounds of potatoes cost thirty cents more than two pounds of potatoes. How much (in dollars) would it cost to buy one pound of potatoes and one pound of apples?

Draw the pictures. In the first case, we have:

P: ---------------------
   |   |  |  |  |  |   |
   ---------------------

A: ---------------------
   |   |   |   |   |   |
   ---------------------

In the second case, you have exactly half as many potatoes, which necessarily must be equal to half as many apples:

P: -----------
   |   |  |  |
   -----------
             |
A: -----------
   |   |   | |
   -----------

The half of the apples is 2.5 pounds, obviously. So three pounds of potatoes is equal to 2.5 pounds of apples, but is thirty cents more than just two pounds of apples. Then how much does a half-pound of apples cost? Then how much does a full pound of apples cost? Then how much does a pound of potatoes cost?

Eliz.

 

[Nicole.ss]

Thank you very much, I didn't solved it for the test but now I get it.

The help I get in this forum is so huge

Thank you everyone involved,
Nicole