Question

Corey's salsa recipe calls for 2 1/2 cups of onions for every 4 pounds of tomatoes Corey Perseus 10 pounds of tomatoes and wonders how many cups of onion eats identify the quantity is represented by the dependent and independent variables in a proportional relationship?

Answer 1

For 10 pounds of tomatoes 6.25 i.e.
`6(1)/(4)` cups of onions required.

Explanation:

Corey's salsa recipe calls for
`2(1)/(2)` cups of onions for every 4 pounds of tomatoes.

If the amount of onions is represented by y in cups and the amount of tomatoes by x in pounds, then the proportional relation between x and y is

y = kx ............. (1)

{Where, amount of tomatoes is the independent variable and amount of onions is the dependent variable}

Now, putting x = 4 pounds and y =
`2(1)/(2)` i.e. 2.5 cups, we get from equation (1) as

2.5 = 4k

⇒ k = 0.625

Now, the equation becomes, y = 0.625x ........ (2)

Now, from equation (2) for, x = 10 pounds, y = 0.625 × 10 = 6.25 cups.

Therefore, for 10 pounds of tomatoes 6.25 i.e.
`6(1)/(4)` cups of onions required. (Answer)