Question

Please solve #24 for me.I’m struggling badly with systems of equations and need some help solving problems with it.Please explain the steps of it as best and basic as possible.

Answer 1

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

`2s+3.50L=163`

• Equation 2: ,the number of L sold was 12 more than the number of ,s.

`L=s+12`

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:

`2s+3.50*\left(s+12\right)=163`

Simplifying the parenthesis we get:

`2s+3.50s+42=163`

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:

`2s+3.50s=163-42`
`5.50s=121`
`s=(121)/(5.50)`
`s=22`

Now that we have s, we just have to replace this value in equation 2:

`L=22+12=34`

Answer:

• Small snow cones: 22

,

• Large snow cones: 34