Question

My question asks; at an ice cream parlor, ice cream cones cost $1.10 and Sundaes cost $2.35. One day the receipts for a total of 172 cones and Sundaes were $294.20. How many cones were sold?

Answer 1

Data:

ice cream cones: x

sundaes: y

Total receipts :T

`T=1.10x+2.35y`

As the total of cones and sundaes is 178:

`x+y=172`

The total receipts were: $294.20

`294.20=1.10x+2.35y`

1. Solve one of the variables in one of the equations:

Solve x in the first equation:

`\begin{gathered} x+y=172 \\ x=172-y \end{gathered}`

2. Use this value of x in the other equation:

`\begin{gathered} 294.20=1.10x+2.35y \\ 294.20=1.10(172-y)+2.35y \\ \end{gathered}`

3. Solve y:

`\begin{gathered} 294.20=189.2-1.10y+2.35y \\ 294.20-189.2=-1.10y+2.35y \\ 105=1.25y \\ (105)/(1.25)=y \\ y=84 \end{gathered}`

4. Use the value of y=84 to find the value of x:

`\begin{gathered} x=172-y \\ x=172-84=88 \end{gathered}`

Then, the ice cream parlor sold 88 cones and 84 sundaes