Question

If paint brushes cost \[\$ 1.50\] each and canvases cost 6 times that much, which of the following represents the cost, in dollars, of \[p\] paint brushes and \[c\] canvases?
A. \[7.5pc\]
B. \[10.5pc\]
C. \[9c + 1.5p\]
D. \[10.5\left( {p + c} \right)\]

Answer 1

Hint: Here the given question is a word problem, we have to find the total cost of both \[p\] paint brushes and \[c\] canvases. First, we need to find the cost of \[p\] paint brushes by multiplying p with cost of each paint brush and find the cost of \[c\] canvases by using the given condition i.e., canvases cost 6 times more than the paint brush and further add a cost of \[p\] paint brushes and \[c\] canvases to get the required solution.

Complete step by step answer:
Consider a given question: The cost of each paint brush \[ = \$ 1.50\]
The cost of each canvas is 6 times much than paint brushes \[ = \$ 1.50 \times 6\]
Hence, the cost of 1 canvas \[ = \$ 9\]
We have to find the total cost of both \[p\] paint brushes and \[c\] canvases to represent it in dollars. Now, find the cost of \[p\] paint brushes is:
\[ \Rightarrow \,\,p \times \$ 1.50\]
\[\therefore \] The cost of \[p\] paint brushes \[ = \$ 1.5p\]
Now, find the cost of \[c\] canvases is:
\[ \Rightarrow \,\,c \times \$ 9\]
\[\therefore \] The cost of \[p\] paint brushes \[ = \$ 9c\]
The total cost is:
\[ \Rightarrow \,\,\$ 1.5p + \$ 9c\]
\[\therefore \,\,\$ \left( {1.5p + 9c} \right)\]
Hence, the total cost of \[p\] paint brushes and \[c\] canvases is \[\$ \left( {1.5p + 9c} \right)\].

Therefore, option C is correct.

Note: In a word problem read carefully each sentence it has information about the given problem that is how we are going to solve it and note down the data’s step by step of each sentence. The selection of mathematical methods will be dependent on each sentence so we have to choose an appropriate method while solving.