Chapter 3, Problem 21MCQ

To determine

To explain: The system of equations that can be used to find the price of paint and primer.

  $\begin{array}{c}\text{F}\text{. }p=r+\frac{1}{2}r\\ p+2r=42\end{array}$

  $\begin{array}{c}\text{G}\text{. }r=p+\frac{1}{2}p\\ p+2p=42\end{array}$

  $\begin{array}{c}\text{H}\text{. }p=r+2r\\ p+\frac{1}{2}r=42\end{array}$

  $\begin{array}{c}\text{I}\text{. }r=p+2p\\ p+\frac{1}{2}=42\end{array}$

Answer to Problem 21MCQ

The system of equations that can be used to find number of tickets sold on each day is $\begin{array}{c}f-t=56\\ f+t=406\end{array}$ . Option F. is correct.

Explanation of Solution

Given information:

Tia spent $\$42$ on 2 cans of primer and 1 can of paint for her room. The price of paint p is $150\%$ of the price of primer r .

Formula used:

To frame system of equations, convert the language of word problem to mathematical statements by assuming the values of unknown as variables.

Calculation:

Consider the provided information that Tia spent $\$42$ on 2 cans of primer and 1 can of paint for her room. The price of paint p is $150\%$ of the price of primer r .

Recall that to frame system of equations, convert the language of word problem to mathematical statements by assuming the values of unknown as variables.

The price of a can of paint is p and price of a can of primer is r .

Then according to the statement that “The price of paint p is $150\%$ of the price of primer r ”, the mathematical statement in terms of variable will be,

  $\begin{array}{c}p=150\%\text{ of }r\\ p=\frac{150}{100}r\\ p=\frac{3}{2}r\\ p=r+\frac{1}{2}r\end{array}$

Now, according to statement that “Tia spent $\$42$ on 2 cans of primer and 1 can of paint for her room”, the equation so formed will be,

  $2r+p=42$

Therefore, the system of equation is,

  $\begin{array}{c}p=r+\frac{1}{2}r\\ p+2r=42\end{array}$

Thus, the system of equations that can be used to find number of tickets sold on each day is

  $\begin{array}{c}p=r+\frac{1}{2}r\\ p+2r=42\end{array}$ .

Option F. is correct.