Question

4) The sum of two numbers is 21. The smaller number is three more than half the larger number. What are the two numbers?

13) You purchase 5 movies and a CD. The cost of the CD is $8.50. Your total bill before tax is $38.45. Write and solve an equation to find the cost of a movie.

Answer 1

4) smaller number is 9, larger number is 12

13) 38.45=5m+8.5

m=5.99

Explanation:

x+y=21 the sum of two numbers is 21

x-3=.5y the smaller number is 3 more than half the larger number

multiply both sides by 2 and you get 2x-6=y

plug that equation into the first equation and you get x+2x-6=21

simplifying you get 3x-6=21 add 6 to both sides and you get 3x=27

x=9 so the smaller number is 9 then you plug that back into the first equation and get y=12

let m be the cost of 1 movie and c be the cost of the cd

38.45=5m+c

38.45=5m+8.5 this is the equation you use

subtract 8.5 from both sides and you get 29.95=5m

divide both sides by 5

5.99=m the answer