Question

The cost of three pants and four shirts is $68.45. If a pant costs $6.85 morethan a shirt, find the cost of a pant and a shirt. Estimate to the nearest wholenumber.

Answer 1

Solution:

Let the cost of a pant and a shirt be represented by x and y respectively.

This implies that

$\begin{gathered} cost\text{ of a pant}\Rightarrow\ \text{ x} \\ cost\text{ of a shirt}\Rightarrow\ \text{ y} \end{gathered}$

Given that the cost of three pants and four shirts is $68.45, this implies that

$3x+4y=68.45\text{ ---- equation 1}$

If a pant costs $6.85 more than a shirt, this implies that

$x=6.85+y\text{ ---- equation 2}$

To find the cost of a pant and a shirt,

step 1: Substitute equation 2 into equation 1.

Thus, we have

$\begin{gathered} 3x+4y=68.45 \\ \Rightarrow3\left(6.85+y\right)+4y=68.45 \\ open\text{ parentheses,} \\ 20.55+3y+4y=68.45 \\ collect\text{ like terms,} \\ 7y=47.9 \\ divide\text{ both sides by the coefficient of y, which is 7} \\ \frac{7y}{7}=\frac{47.9}{7} \\ \Rightarrow y=6.842857143 \end{gathered}$

step 2: Substitute the value of y into equation 2.

Thus, we have

$\begin{gathered} x=6.85+y \\ =6.85+6.842857143 \\ \Rightarrow x=13.69285 \\ \end{gathered}$

Hence, to the nearest whole number, the respective cost of a pant and a shirt is

$\begin{gathered} x=\ 14 \\ y=\ 7 \end{gathered}$