Liam bought a picture frame that costs $12 plus 8% sales tax. HE wrote the expression 1.08(12) to find his total cost.

Which expression is equivalent to the total cost?

A) 12 + 0.08
B) (12 + 0.08)12
C) 1 + .0.08(12)
D) (1 + 0.08)12

(1 + 0.08) = 1.08

The correct expression equivalent to the total cost is D) (1 + 0.08)12.

To find the total cost, Liam needs to add the sales tax to the original cost of the picture frame. The sales tax is calculated by multiplying the original cost by the tax rate (8%).

So, Liam's total cost can be found using the expression 1.08(12).

Now let's compare the given expressions and see which one is equivalent to 1.08(12):

A) 12 + 0.08: This expression only adds the tax rate of 0.08 to the original cost, so it's not equivalent to 1.08(12).

B) (12 + 0.08)12: This expression multiplies the sum of the original cost and the tax rate by 12. It's not equivalent to 1.08(12) since it's multiplying the sum by 12 instead of multiplying the original cost by 1.08.

C) 1 + 0.08(12): This expression adds 1 to the product of the original cost and the tax rate. It's not equivalent to 1.08(12) since it's adding 1 to the product instead of multiplying the original cost by 1.08.

D) (1 + 0.08)12: This expression adds 1 to the tax rate and then multiplies the sum by 12. It is equivalent to 1.08(12) because 1 + 0.08 equals 1.08, and then multiplying by 12 gives the same result as multiplying the original cost by 1.08.

Therefore, the expression that is equivalent to the total cost is option D) (1 + 0.08)12.