sundaes for $2 and splits for $3. the shop sold 8 more sundaes then banana splits.they made a total of $156.how many sundaes and banana spits did they sell?

Question

write two equations then solve using substatution or elimination

Answer 1

Hey Alex.

 

Let's set up some variables.

 

S = number of sundaes sold

B = number of (banana) splits sold

 

Cs = cost of a sundae ($2)

Cb = cost of a (banana) split ($3)

 

We know the shop sold 8 more sundaes than banana splits. That means that:

 

S = B + 8

 

We know they made a total of 156 in sales. That means that:

 

Cs*S + Cb*B = 156

2*S + 3*B = 156

 

So now we have 2 equations and 2 unknowns.

 

S = B + 8

2S + 3B = 156

 

Let's substitute.

 

2(B + 8) + 3B = 156

 

2B + 16 + 3B = 156

 

5B = 140

 

B = 28.

 

S = 28 + 8 = 36.

 

There were 36 sundaes and 28 splits sold.

 

Always a good idea to check your work.

 

2*36 + 3*28 should equal 156.

 

72 + 84 = 156. Check.

 

36 should be 8 more than 28.

 

36 - 28 = 8. Checkmate.

 

Hope this helps.