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Erin bought 4 jars of jelly and 6 jars of peanut butter for $19.32. Adam bought 3 jars of jelly and 5 jars of peanut butter for $15.67. Find the cost of a jar of peanut butter.

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Answer:

Step-by-step explanation:

X = cost of PB  

Y = cost of J

 

6X + 4Y = 1932  <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

 

Dividing everything in the first equation by 2:

 

3X + 2Y =  966 <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

 

 

Elimination method... let's multiply the first equation by 3 and the second equation by -2.

 

   9X +   6Y =   2898

-10X + -6Y  = -3134

 

-X = -236

X =  236 --> so the price of the PB is 236 pennies or $2.36

 

Plugging into the second equation as the numbers are a bit smaller,

 

5X + 3Y = 1567

5(236) + 3Y = 1567

1180 + 3Y = 1567

3Y = 387

Y = 129. So the price of the jelly is 129 pennies or $1.29.

 

Now we check:  4 x $1.29 + 6*2.36 = $19.32

                       3 x $1.29 + 5 x 2.36 = $15.37

 

The answers are verified and highlighted in bold.

 

 

 

 

6X + 4Y = 1932  <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

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