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.

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