Question

3. Caleb has $25 to spend on prizes for a game at the school fair. Lip balm costs $1.25 each, and mini-notebooks cost $2.50 each.

a. Write a linear equation in STANDARD FORM that can be used to determine how many of each prize she can buy.
b. Graph the equation using x- and y- intercepts.

Answer 1

linear equation in Standard form that can be used to determine how many of each prize Caleb can buy is
`1.25x+ 2.50y = 25`

Explanation:

Given:

Total cost spent on prizes for games = $25

Cost of one lip balm = $1.25

Cost of one mini notebook = $2.50

A) linear equation in STANDARD FORM that can be used to determine how many of each prize she can buy.

Let the number of lip balms be x and the number of mini note books be y. Then

`1.25x+ 2.50y = 25`

B. Graph the equation using x- and y- intercepts.

Now by trial and error method

`1.25(0)+ 2.50(10) = 25`

`1.25(2)+ 2.50(9) = 25`

`1.25(4)+ 2.50(8) = 25`

`1.25(6)+ 2.50(7) = 25`

`1.25(8)+ 2.50(6) = 25`

`1.25(10)+ 2.50(5) = 25`

`1.25(12)+ 2.50(4) = 25`

`1.25(14)+ 2.50(3) = 25`

`1.25(16)+ 2.50(2) = 25`

`1.25(18)+ 2.50(1) = 25`

`1.25(20)+ 2.50(0) = 25`

Thus Caleb can buy 0,2,4,6,8,9,10,12,14,1,6,18,20 lip balms and

0,1,2,3,4,5,6,7,8,9,10 mini note books respectively

Now plotting these value in the graph, we get the below graph