Data
• Small cones (s): $2
,• Large cones (L): $3.50
,• Total sold (T): $163
,• The number of L sold was 12 more than the number of ,s.
Procedure
We have to build a system of equations based on the information given.
• Equation 1:, she sold $163 of small and large cones
[tex]2s+3.50L=163[/tex]• Equation 2: ,the number of L sold was 12 more than the number of ,s.
[tex]L=s+12[/tex]As we have L isolated in the second equation, it is convenient to use this expression in the first equation to have it in terms of one variable:
[tex]2s+3.50\times\left(s+12\right)=163[/tex]Simplifying the parenthesis we get:
[tex]2s+3.50s+42=163[/tex]As we have two terms with an s we can group in each side of the equation the common terms and simplify them as follows:
[tex]2s+3.50s=163-42[/tex][tex]5.50s=121[/tex][tex]s=\frac{121}{5.50}[/tex][tex]s=22[/tex]Now that we have s, we just have to replace this value in equation 2:
[tex]L=22+12=34[/tex]Answer:
• Small snow cones: 22
,• Large snow cones: 34