Chapter 3.7, Problem 1P

To determine

To calculate:the unknown in the given charts.

Answer to Problem 1P

12

Explanation of Solution

Given:

	$\text{Number}\times \text{Price = cost}$
Fancy	$f$	$?$	$?$
Plain	$?$	$?$	$?$

Total no. of students = 30

Plain pennants cost = 4

Fancy pennants cost = 8

Total bill of the pennants=168

Calculation:

Let the no. of students bought plain pennants be = $x$

Let the no. of students bought fancy pennants be = $y$

Total no. of student bought both pennants = $x+y=30eq.\left(1\right)$

Cost of plain pennants bought by $x$ student = $4x$

Cost of fancy pennants bought by $y$ student = $8y$

Total bill of the pennants = $4x+8y=168eq.\left(2\right)$

now multiply the eq.1 with 4

  $4x+4y=120eq\left(3\right)$

Now subtracting eq.3 from eq.2

  $\begin{array}{l}\text{}\underset{\_}{\begin{array}{l}4x+8y=168\\ 4x+4y=120\\ ---\end{array}}\\ 0+4y=48\\ y=\frac{48}{4}\\ y=12\end{array}$

Now substitute the value of $y$ in eq.1 then we get

  $\begin{array}{l}x+y=30\\ x+12=30\\ x=30-12\\ x=18\end{array}$

	$\text{Number}\times \text{Price = cost}$
Fancy	$12$	$8$	$96$
Plain	$18$	$4$	$72$

So, 12 student bought fancy pennants