Question

Your club is ordering enrollment gifts engraved with your club logo. Keychains cost $5 each. Wristbands cost $2 each. You have a budget of $100 for the gifts. The equation 5x+2y=$100 models the total cost, where x is the number of key chains and y is the number of wristbands

Answer 1

Part A) The y-intercept is the point (0,50) and the x-intercept is the point (20,0)

The graph in the attached figure

Part B) The club can order 5 wristbands

Explanation:

The questions are

A. Graph the equation. Intercepts.

B. Your club decides to order 18 key chains. How many wristbands can you order?

Part A) Graph the equation. Intercepts.

Let

x -----> is the number of key chains

y -----> is the number of wristbands

we have

The equation that model the total cost is

`5x+2y=100`

To graph the line, find out the intercepts first

Find out the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

substitute in the linear equation and solve for y

`5(0)+2y=100`

`2y=100`

`y=50`

The y-intercept is the point (0,50)

Find out the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

For y=0

substitute in the linear equation and solve for x

`5x+2(0)=100`

`5x=100`

`x=20`

The x-intercept is the point (20,0)

To graph the line, plot the intercepts ad join the points

see the attached figure

Part B) Your club decides to order 18 key chains. How many wristbands can you order?

Remember that

x -----> is the number of key chains

y -----> is the number of wristbands

so

we have

For x=18

Substitute in the equation the value of x and solve for y

`5(18)+2y=100`

`90+2y=100`

subtract 90 both sides

`2y=100-90`

`2y=10`

divide by 2 both sides

`y=5`

therefore

The club can order 5 wristbands