Question

you want to buy desserts for your sisters birthday party. At the grocery store it costs $6 for a package of cupcakes and 4$ for a package of cookies. write a linear equation to represent the number of items you can buy if she spends $48

Answer 1

Part a)
`6x+4y=48`

Part b) The graph in the attached figure

Part c) (6,3) and (4,6)

Explanation:

Part a) Write a linear equation to represent the number of items you can buy if she spends $48

Let

x ----> number of package of cupcakes you can buy

y ---> number of package of cookies you can buy

we know that

The number of package of cupcakes you can buy multiplied by it cost ($6 for a package) plus the number of package of cookies you can buy multiplied by it cost ($4 for a package) must be equal to $48

so

The linear equation that represent this problem is

`6x+4y=48`

Part b) Graph the equation

To graph the line we need two points

Find the intercepts

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

`6x+4(0)=48` ---->
`x=8`

the x-intercept is the point (8,0)

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

`6(0)+4y=48` ---->
`y=12`

the y-intercept is the point (0,12)

Plot the intercepts and join the points to graph the line

see the attached figure

Part c) State two possible solutions in the context of the problem

1) First possible solution

the ordered pair (6,3)

That means

You can buy 6 package of cupcakes and 3 package of cookies

Verify in the linear equation

`6(6)+4(3)=48`

`48=48` ---> is true

therefore

The ordered pair is a solution of the linear equation

2) Second possible solution

the ordered pair (4,6)

That means

You can buy 4 package of cupcakes and 6 package of cookies

Verify in the linear equation

`6(4)+4(6)=48`

`48=48` ---> is true

therefore

The ordered pair is a solution of the linear equation