Question

Question #f9561

Answer 1

See a solution process below:

Explanation:

We can write an equation using the variable names in the problem as:

`c = b * p`

Where:

`c` is the total cost of the bananas.

`b` is the price per pound for the bananas

`p` is the weight of the bananas.

Substituting from the problem for `c` and `p` we can solve for `b`:

`$2.50 = b * 5"lbs"`

`($2.50)/color(red)(5"lbs") = (b * 5"lbs")/color(red)(5"lbs")`

`($0.50)/("lbs") = (b * color(red)(cancel(color(black)(5"lbs"))))/cancel(color(red)(5"lbs"))`

`($0.50)/("lbs") = b`

`b = ($0.50)/("lbs")`

We can substitute this into the original equation to give us the equation for bananas:

`c = ($0.50)/("lbs") * p`

We can now determine the price for `8"lbs"` by substituting for `p` and calculating `c`:

`c = ($0.50)/("lbs") * p` becomes:

`c = ($0.50)/("lbs") * 8"lbs"`

`c = ($0.50)/color(red)(cancel(color(black)("lbs"))) * 8color(red)(cancel(color(black)("lbs")))`

`c = $4.00`

Mrs. Baker would pay $4.00 for 8 pounds of bananas at the same price.

Answer 2

This is a ratio. Set up the values in an equation that will give the desired dimensional amount.
`"cost" = $0.50/"pound"`
`$4.00`

Explanation:

In this case, we must first determine the ratio: `"cost"/"pound"`.
This is `"cost" = $2.50/5 "pounds" = $0.50/"pound"`

NOW we can use this ratio to calculate ANY price for any weight of bananas. Applied to the question of how much 8 pounds of bananas would cost, we have:
`$0.50/"pound" xx 8 "pounds" = $4.00`

Answer 3

`$4`

Explanation:

We first must determine the cost for one pound of bananas.

We can do this by dividing `(2.50)/5=0.5`. So one pound of bananas cost `$0.50`

We can then write a generalized equation:

`C=0.5p`

where `C` is the total cost and `p` is the amount of pounds of the bananas.

We can try out this equation by substituting `5` for `p` in the equation. This should yield `2.50`

`C=0.5(5)`

`C=2.50`

Thus, to answer your other question: To find the cost for `8` pounds bananas, we substitute `8` for `p` in our equation:

`C=0.5(8)`

`C=4`

So Mrs. Baker would pay `$4` for `8` pounds of bananas