Q40. - Algebra 2

Question

All $28$ members in Crestview High School’s Ski Club went on one-day ski trip. Members can rent skis for $\backslash ( 16.00$ per day or snowboards for $\backslash ) 19.00$ per day. The club paid a total of $\$ 478$ for rental equipment.

 How many members rented skis and how many rented snowboards? 

Step-by-Step Solution

Answer

$18$ members rented skis and $10$ members rented snowboards.

Step-1 – Apply the concept of system of equations

A set of two or more equations with the same variables is called a system of linear equations. The ordered pairs that satisfy all the equations in the system is called as solution of the equations.

Step-2 – Formation of the equations

Here, x represents the number of members that rented skis and y represents the number of members that rented snowboards. The equations so formed according to the question are:

$\begin{array}{c}x+y=28\\ 16x+19y=478\end{array}$

Step-3 – Apply the substitution method of solving equations

The algebraic method of substitution involves solving the one of the two equations for one variable in terms of other variable and then substituting the expression so formed for the variable in the second equation.

Step-4 – Solving one equation for x in terms of y

To solve the equation $x+y=28$ for x in terms of y, subtract y from both sides as shown below.

$\begin{array}{c}x+y-y=28-y\\ x=28-y\end{array}$

Step-5 – Substitute the expression

Now, substitute $x=28-y$ in the equation $16x+19y=478$ and solve.

$\begin{array}{c}16\left(28-y\right)+19y=478\\ 448-16y+19y=478\\ 3y=30\\ y=10\end{array}$

Thus, the value of y is $10$.

Step-6 – Substitute the value of variable

To find the value of x, substitute $y=10$ in the equation $x+y=28$ and then solve as shown.

$\begin{array}{c}x+y=28\\ x+10=28\\ x=28-10\\ x=18\end{array}$

Thus, the value of x is $18$.

Hence, $18$ members rented skis and $10$ members rented snowboards.