Question

Customer at a craft store buying a blank canvas and a set of brushes the customer has two coupons one coupon is valid for 35% off all canvases and the other is valid for 20% off the entire purchase the customer can only use one coupon let’s represent the original price of the canvas and B represent the price of the set of brushes write two expressions that represent 35% off all canvases coupon write two expressions that represent 20% off the entire purchase coupon if the original cost of the canvas is $12 and the set of brushes is $16 which option would be the better choice explain

Answer 1

To represent the 35% off coupon for all canvases, the expression is B - 0.35B or B(1 - 0.35).

To represent the 20% off coupon for the entire purchase, the expression is (B + 16) - 0.2(B + 16) or (B + 16)(1 - 0.2).

If the original cost of the canvas is $12 and the set of brushes is $16, the 35% off coupon is the better choice with a final cost of $7.80.

Step-by-step explanation:

Solving both the cases:

To represent the 35% off coupon for all canvases, you can multiply the original price of the canvas by 0.35 and subtract that value from the original price.

So the expression would be: B - 0.35B.

Another way to write this expression is: B(1 - 0.35) or B(0.65).

To represent the 20% off coupon for the entire purchase, you can multiply the sum of the original price of the canvas and the price of the set of brushes by 0.2 and subtract that value from the sum.

So the expression would be: (B + 16) - 0.2(B + 16).

Another way to write this expression is: (B + 16)(1 - 0.2) or (B + 16)(0.8).

If the original cost of the canvas is $12 and the set of brushes is $16, we can now substitute these values into the expressions to see which option is better:

35% off: B - 0.35B

= 12 - 0.35(12)

= 12 - 4.2

= $7.80

20% off: (B + 16) - 0.2(B + 16)

= (12 + 16) - 0.2(12 + 16)

= 28 - 0.2(28)

= 28 - 5.6

= $22.40

Based on these calculations, the 35% off coupon would be the better choice as it gives a lower final cost of $7.80 compared to the 20% off coupon's final cost of $22.40.