A bakery sells 10 ounce bags of nuts for $3.26 per bag. They sell 8 ounce bags of mints for $4.10 per bag. They receive a check for $88.48 for an order of 22 i

Question

A bakery sells 10 ounce bags of nuts for $3.26 per bag. They sell 8 ounce bags of mints for $4.10 per bag.  They receive a check for $88.48 for an order of 22 items. How many items did they sell? 

 

Define your variables. Set up a system of equations. Solve the system of equations.

Answer 1

Assuming the question being asked is how

many bags of nuts and how many bags of

mints were in this order.

 

The weight of each bag does not matter.
What is important is the number of bags.

 

Let n =  number of bags of nuts

      m = number of bags of mints

22 items were in the  order =>

(1)  n + m = 22

 

The cost of the order was $88.48

(2) 3.26n + 4.10m = 88.48

     326n + 410m = 8848

     163n + 205m = 4424

 

The system of equations is (1) and (2)

 

Solve the equation using substitution.

 

From (1), n = 22 - m

 

Substitute this value into (2):

163(22 - m) + 205m = 4424

3586 - 163m + 205m = 4424

42m = 838

m = 419/21 = 19 20/21 ≈ 19.95 bags of mints

 

Then n = 43/21  = 2 1/21 ≈ 2.05 bags of nuts

 

The problem didn't indicate that they were whole bags.

 

If whole bags are intended, then 20 bags of mints

and 2 bags of nuts would be in the order.

The cost of the order should been $88.52, with a

lost or bill for $0.04

 

There is also the possibility that only 19 bags of mints

and 3 bags of nuts were shipped.

In this case the cost would have been $87.68 and

customer would be given $0.80 as change.