What is the result of this problem?

Question

A bag of dozen grapefruit was selling for $6.60. The produce manager added some grapefruit to the bag but did not change the $6.60 price. The price of a dozen grapefruit now was actually $4.40. How many grapefruit were added to the bag?

Answer 1

Hi George,

 

Let's begin by assigning a letter to represent our unknown:

    x = # apples added to bag without price change

 

Next, let's set up this proportion of equivalent ratios, which we can use to solve for our unknown (x):

    price : initial number = price : corrected number

    6.60 : 12 = 4.40 : 12 - x

 

Note that the "corrected number" is the initial dozen minus the number of apples (x), which should NOT have been added to the bag without change in price.

 

Next, let's solve for our unknown (x):

    6.60/12 = 4.40/(12 - x)

    (6.60)(12 - x) = (12)(4.40)

    79.2 - 6.6x = 52.8

    6.6x = 79.2 - 52.8

    6.6x = 26.4

    x = 26.4/6.6

    x = 4 apples added to bag without price change

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

Answer 2

Step 1: Process the given information. "Some grapefruit was added to the bag of 12, to give a price of $6.60."

Step 2: Translate this into math language. x + 12 = 6.60

Step 3: Create a ratio to relate the given pieces of information. (x/12)/6.60 = 12/(4.60) because the problem says,

"Some grapefruit was added to the bag of 12, to give a price of $6.60." = "Now, the price of 12 grapefruit is $4.40" We are relating (number of grapefruit/price) = (number of grapefruit/price).

Step 4: Solve the equation. (x/12)/6.60 = 12/(4.60)

                                          4.40(x + 12) = 12/(4.60)

                                          4.40x + 52.8 = 79.2

                                          4.40x = 79.2 - 52.8

                                          4.40x = 26.4

                                          x = 6

Therefore the produce manager had added six grapefruit to the original bag.