Question

Tasty bakery sells three kinds of cookies Chocolate chip at $.30 each oatmeal raisin at $.35 each and peanut butter at $.40 each. Candace buys some of each kind and chooses twice as many peanut butters as chocolate chip. If she spends $5.75 on 16 cookies, how many oatmeal raisin cookies did she buy?

Answer 1

She bought 7 oatmeal raisin cookies.

Explanation:

Let us assign letters to the unknowns:

Number of chocolate chip cookies = C

Number of oatmeal raisin cookies = O

Number of peanut butter cookies = P

Create one equation that gives the relation between the number of chocolate chip cookies to the number of peanut butter ones:

P = 2 C equation (1)

Now an equation for the total number of cookies she bought (16):

P + C + O = 16 equation (2)

Now an equation for the total value of the purchase, and multiplying the number bought of each cookies times its price:

$5.75 = 0.3 C + 0.35 O + 0.4 P equation (3)

Now we have 3 equations and 3 unknowns, and proceed to solve first by substituting P with "2 C" as per equation (1) in the other two equations:

Equation (2) becomes: 2 C + C + O = 16, therefore: 3 C + O = 16, and then we solve for O in terms of C:

O = 16 - 3 C equation (4)

We use equations (1) and (4) to re-write equation 3 all in terms of C:

5.75 = 0.3 C + 0.35 (16 - 3C) + 0.4 (2 C)

5.75 = 0.3 C + 5.6 - 1.05 C + 0.8 C

5.75 - 5.6 = 0.05 C

0.15 = 0.05 C

C = 3

Then she bought 3 chocolate chip cookies, which means (from equation (4), that she bought :

O = 16 - 3 * 3 = 16 - 9 = 7

7 oatmeal raisin cookies.