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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.

Write and solve a system of equations that models the problem and shows which class earned more money and how much more money did that class earn.

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Аноним Аноним · Answer 1 · 2019-01-28T07:03:03+01:00

Solution:

Let number of Cookies sold by Mrs. Johnson’s class = x

Let number of Cookies sold by Mrs. Smith class = y

Total Number of Cookies sold by Mrs. Johnson’s class and Mr. Smith’s class=53

Writing in terms of equation the statement which is given above

1. x + y = 53 ⇒y= 53-x

2. 2.50 x + 1.50 y = 105.50

Substituting the value of y, in equation 2, we get

⇒2.50 x + 1.50 (53-x)= 105.50

⇒ 2.50 x + 1.50 × 53 - 1.50 x= 105.50→→[Using Distributive property of addition with respect to multiplication]

Combining like terms using Operations (Addition, Subtraction)

⇒1. 0 x + 79.50=105.50

⇒ x =105.50-79.50

⇒ x= 26

Putting the value of x, in equation (1)

26 + y=53

y= 53 - 26

y= 27

Money earned by Mrs. Johnson’s class = 26 × $2.50=$ 65

Money earned by Mr. Smith’s class = 27 × $1.50=$ 40.50

So, Mrs. Johnson’s class earned more money.

Amount of money that Mrs. Johnson’s class earned exceeds than Mr. Smith’s class= $ 65 - $ 40.50= $ 24.50