Question

Todd orders pictures from a photographer. Each picture costs $7.50. A one-time shipping fee of $3.25 is added to the cost of the order. The total cost of Todd's order before tax is $85.75. How many pictures did Todd order? Solve this problem using two different methods or strategies. Label your strategies.

Answer 1

• Rate of change=$7.5
• One time fee(Y intercept)=$3.25

Equation in slope intercept form

• y=mx+b
• y=7.5x+3.25

So

Total paintings is x

• 85.75=7.5x+3.25
• 7.5x=82.5
• x=11 paintings

Answer 2

11 pictures

Explanation:

Method 1

Create an algebraic equation from the given information, defining the unknown quantity as a variable, then solve for the variable.

Given:

• Cost of one picture = $7.50
• Shipping fee (one time) = $3.25
• Total cost of order = $85.75

Let x = number of pictures ordered

⇒ Cost of one picture × number of pictures ordered + shipping fee = total

⇒ 7.5x + 3.25 = 85.75

⇒ 7.5x + 3.25 - 3.25 = 85.75 - 3.25

⇒ 7.5x = 82.50

⇒ 7.5x ÷ 7.5 = 82.50 ÷ 7.5

⇒ x = 11

Therefore, Todd ordered 11 pictures.

Method 2

Logic and trial and error.

Given:

• Cost of one picture = $7.50
• Shipping fee (one time) = $3.25
• Total cost of order = $85.75

If the shipping fee is a one time cost, then if we subtract this from the total cost of the order, we know how much Todd spent on the pictures alone:

⇒ $85.75 - $3.25 = $82.50

We have been told that each picture costs $7.50.

Therefore, 10 pictures costs $75.00 (when multiplying by 10, we simply move the decimal point one place to the right).

$75.00 is less than $82.50. So what happens if we add another $7.50 to $75.00?

⇒ $75.00 + $7.50 = $82.50

Therefore, Todd ordered 10 + 1 = 11 pictures.