Gretchen and her friend Hayley bought three bags of apples and three bunches of bananas from the fruit vendor. Gretchen and Hayley want to find the total number of pieces of fruit that they bought. Gretchen thinks she should multiply 3 by the number of apples in each bag, x, and add it to 3 times the number of bananas in each bunch, y, to find the total number of pieces of fruit. Hayley thinks Gretchen should add the number of apples in each bag, x, to the number of bananas in each bunch, y, and then multiply that sum by 3.

The total number of pieces of fruit that they bought should be 72.

Here we assume 3 bags of apples with 4 apples in each bag  

And, 3 bunches of bananas with 4 bananas in each bunch  

Now  

= 12 + 12

= 24 pieces of fruit

Since

4 + 4 + 4  (12)  apples   +   4 = 4 + 4  (12)  bananas

So,

= 12 + 12

= 24  

here we need to multiplied by 3

So,  

= 72

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Gretchen thinks she should multiply 3 by the number of apples in each bag, x, and add it to 3 times the number of bananas in each bunch, y, to find the total number of pieces of fruit.

Step-by-step explanation:

Let's imagine 3 bags of apples with 4 apples in each bag  (3 x 4 = 12)

Let's imagine 3 bunches of bananas with 4 bananas in ea. bunch  (3 x 4 = 12)

Thus, 12 + 12 = 24 pieces of fruit

vs.

4 + 4 + 4  (12)  apples   +   4 = 4 + 4  (12)  bananas

Thus, 12 + 12 = 24  

24 x 3 = 72    >>  Uh - Oh !!

this is a direct variation proportion. y = kx

y is the total amount due, k is the constant of variation, and x is the number of texts sent.

plug in the 3.20 and the 16 to solve for the "k". this is the constant of proportionality. it is the value that will not change.

3.20 = k(16). solving you get $.20 per text.

the equation would then be y = .20x