Question

If a store sells paint brush at \[\$ 1.50\] each and canvases at six times price of paintbrush, then the total cost of p paintbrushes and c canvases, in dollar is
A.\[7.5pc\]
B.\[10.5pc\]
C.\[9c + 1.5p\]
D.\[10.5\left( {p + c} \right)\]

Answer 1

Hint: This is a very easy to solve question. We just have to find the cost of canvas only because the cost of paintbrush is already given to us. After finding the cost of one canvas and one paint brush we will multiply it with the number of canvases and paint brushes asked or given respectively. That will be the answer to the question.

Complete step by step solution:
Given that cost of a paint brush is \[\$ 1.50\]
Cost of a canvas is six times that of the paintbrush. So cost of canvas will be
\[ = 1.50 \times 6 = \$ 9\]
But we are given with p paintbrushes. So cost of paint brushes will be
\[ = \$ p \times 1.50\]
Cost of c canvases will be given by
\[ = \$ c \times 9\]
Now total cost of p paintbrushes and c canvases will be equal to
\[ = p \times 1.50 + c \times 9\]
That is on rearrangement can be written as \[ = 9c + 1.5p\]
Thus option C is the correct answer.
So, the correct answer is “Option C”.

Note: Note that in option D they have given the addition of the constants in the answer. But we cannot add two different materials costs together. The cost of a paintbrush is not the same as the cost of canvas. So we cannot add two different variables. So that is not the correct answer.
Talking about option A they just have taken the cost of one paintbrush as \[\$ 1.50\] and that of one canvas as \[\$ 6\] whereas that is not rate that is just six times as that of rate of paintbrush. So that option is also wrong. Rather they have taken products between p and c also. Same mistake is made in option B also.