Chapter 4.6, Problem 43HP

To determine

To calculate: the number of medium cones sold by Yogurt Shoppe.

Answer to Problem 43HP

Option C is correct.

Explanation of Solution

Given information:

Small, $0.89; medium, $1.19; large, $1.39.

Santos sold 52 cones. He sold seven more medium cones than small cones. He sold $58.98 cones.

Formula used:

Substitution property is used.

Calculation:

Let the number of small cones sold = x

Let the number of medium cones sold = y

Let the number of large cones sold = z

According to the question ,

Total number of cones sold:-

  $x+y+z=52$ (i)

Total money:-

  $x(0.89)+y(1.19)+z(1.39)=58.98$ (ii)

Also,

  $x=y-7$ (iii)

Putting value of x in equation (i) and (ii) we get,

  $\begin{array}{l}=y-7+y+z=52\\ =2y+z=52+7\\ =2y+z=59\end{array}$ (iv)

  $\begin{array}{l}=(y-7)(0.89)+y(1.19)+z(1.39)=58.98\\ =0.89y-6.23+1.19y+1.39z=58.98\\ =0.89y+1.19y+1.39z=58.98+6.23\\ =2.08y+1.39z=65.21\end{array}$ (v)

From equation (iv) we get,

  $z=59-2y$ (vi)

Substituting value of z in equation (v)

  $\begin{array}{l}=2.08y+1.39(59-2y)=65.21\\ =2.08y+82.01-2.78y=65.21\\ =2.08-2.78y=65.21-82.01\\ =-\frac{0.7y}{0.7}=-\frac{16.8}{0.7}\\ =y=24\end{array}$

Substituting value of y in equation (iii) and (vi)

  $\begin{array}{l}=z=59-2(24)\\ =z=59-48\\ =z=11\end{array}$

  $\begin{array}{l}=x=24-7\\ =x=17\end{array}$

Hence, the number of medium cones sold was 24.