Question

Mrs. Johnson’s class sold cookies for $2.50 each and Mr. Smith’s class sold popcorn for $1.50 each. Together, the classes sold 53 items and earned $105.50 for their school. (YOU MUST SHOW ALL WORK TO GET FULL CREDIT!!!)3.

(a)Write and solve a system of equations that model the problem. Show all your work.
(b)Which class earned more money?
(c)How much more money did that class earn?

Answer:

Answer 1

c+p = 53

2.5c+1.5p = 105.5

p = 27

c= 26

Mrs. Johnson earned 65

Mr Smith earned 40.5

Mrs Johnson earned 24.50 more

Explanation:

Let c = cookies sold

p = popcorn sold

The number of items sold is 53

c+p = 53

The total cost of the items sold is 105.50

The number of cookies sold times 2.50 plus the number of popcorn sold times 1.50 = 105.50

2.5c+1.5p = 105.5

System of equations:

c+p = 53

2.5c+1.5p = 105.5

Multiply the second equation by 10 to clear the decimals

10 *(2.5c+1.5p) = 10*105.5

25c+15p = 1055

Divide by 5

25c/5 +15p/5 = 1055/5

5c+3p =211

Multiply equation 1 by -5

-5(c+p)=-5*53

-5c-5p=-265

Add the equations

5c+3p =211

-5c-5p=-265

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-2p = -54

Divide by -2

-2p/-2 = -54/-2

p = 27

Now we need to find c

c+p = 53

c+27 = 53

Subtract 27 from each side

c+27-27 = 53-27

c= 26

Mrs. Johnson earned the number of cookies times 2.5

c* 2.5

26*2.5 =65

Mr Smith earned the number of popcorn times 1.5

p*1.5

27*1.5

40.5

Mrs Johnson earned 65-40.5 = 24.50 more