Question

Story Problems

Answer 1

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.

Answer 2

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.