Jim and Dwight went to the paint store together. Jim bought 6 cans of paint and 1 paintbrush for $67. Dwight bought 4 cans of the same paint and 3 of the same type of paintbrushes. Dwight's total cost was $54. a. Write a linear equation to represent Jim's purchase and another to represent Dwight's purchase. Let x represent the cost of a can of paint and y represent the cost of a paint brush.

b. Solve the system of equations using substitution.

c. What was the cost for a can of paint? The cost of a paintbrush?

A can of paint cost $10.50 and a paintbrush costs $4

Step-by-step explanation:

Using x as the cost of a can of paint and y as the cost of a paint brush, we can write the following system of equations:

6x+y=67

4x+3y=54

We can isolate y in the first equation which gives us:

y=-6x+67

Then we can solve using substitution (substitute -6x+67 for y):

4x+3(-6x+67)=54

4x-18x+201=54

Combine like terms

-14x+201=54

Subtract 201 from both sides

-14x=-147

Divide both sides by -14

x=10.5

Then plug 10.5 back in for x:

y=-6(10.5)+67

y=-63+67

y=4

A can of paint cost $10.50 and a paintbrush costs $4

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

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