Story Problems

3. Lesley bought 4 bags of pretzels and 2 boxes of granola bars for $13.50. Landon bought 1 bag of pretzels and 5 boxes of granola bars for $17.55. What is the cost for one bag of pretzels? What is the cost for a box of granola bars?

4. Savelots offers two types of baseball bats. the wood bats sell for $24 and the metal bats sell for $30. In one day, savelots sold 23 baseball bats. the receipts for those bats totaled $606. How many of each type of bat were sold?

Problem 3: Let x = price of bag of pretzels Let y = price of box of granola bars

We have Lesley's purchase: 4x+2y=13.50

And Landon's: 1x+5y=17.55

We can use the elimination method. Let's negate Landon's purchase by multiplying by - 1. - 1x-5y=-17.55

We add this four times to Lesley's purchase to eliminate the x variable.

2y-20y=13.50-70.2

-18y=-56.7

y = $3.15 = Price of box of granola bars

Plug back into Landon's purchase to solve for pretzels.

x+5*3.15=17.55

x+15.75=17.55

x = $1.80 = price of bag of pretzels

Problem 4.

Let w = number of wood bats sold

Let m = number of metal bats sold

From sales information we have: w + m = 23

24w+30m=606

Substitution works well here. Solve for w in the first equation, w = 23 - m, and plug this into the second.

24 * (23-m) + 30m=606

552-24m+30m=606

6m=54

m=9 = number of metal bats sold

Therefore since w = 23-m, w = 23-9 = 14. 14 wooden bats were sold.

3. x-pretzels

y-granola

Lesley: 4x+2y=13.5

Landon: 1x+5y=17.55⇒x=17.55-5y

4 * (17.55-5y) + 2y=13.5⇒70.2-18y=13.5

x=17.55-5y

18y=56.7⇒y=3.15

x=17.55-5y⇒x=17.55-5*3.15⇒x=1.8

The cost for one bag of pretzels is $1.8, the cost for a box of granola bars is $3.15.

4. The wood bats: x-$24

The metal bats: y - $30

Savelots sold 23 baseball bats: x+y=23

The receipts for those bats totaled $606: $24x+$30y=$606

x+y=23⇒x=23-y

24x+30y=606

x=23-y

24 * (23-y) + 30y=606⇒552-24y+30y=606

x=23-y

6y=54⇒y=9

x=14

14 wood bats and 9 metal bats were sold.