Question

consider the following situation: Mr. Richards wants to buy disposable masks for his family. Elure masks cost $1.50 and white masks cost $2.50. He has $45 to spend and wants to buy a total of 20 masks. 12. Define your variables and write an equation to represent the number of masks Richards is buying. 13. Using the same variables write an equation to represent the cost of the masks Richards is buying. 14. Choose either substitution or elimination and solve the system of equations you have created to determin many of each color Richards can buy. Show all of your steps.

Answer 1

Variables are

X= white masks

Y= Elure masks

then write equations

12) X + Y = 20. (number of masks Richard buys)

and

13) 2.50X + 1.50Y= 45. (Cost of masks)

Now solve this system of 2 equations,

by substitution

then

X = 20 - Y

replace

2.50( 20-Y) + 1.50Y = 45

solve for Y

50 - 2.50Y + 1.50Y = 45

Y= (50-45)/ ( 2.5- 1.5) = 5/1= 5

Now find X

X= 20- 5 = 15

Second part, by elimination

multiply by (-2.50) and add both equations

(-2.50X - 2.50Y ) + (2.50X + 1.50Y ) = -50 + 45

then now eliminate X

-2.50Y + 1.50Y = -5

then

Y= -5/(-2.50+1.50)= -5/-1= 5

and

X= 15

14) Then answer is

Richard buyed

15 white masks

5 elure masks