SOLUTION: 10 balls and 1 ball bag purchased for $155. 12 balls and 2 ball bags purchased for $189. How much does 1 ball cost and how much does 1 ball bag cost?

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Question 731512:
10 balls and 1 ball bag purchased for $155. 12 balls and 2 ball bags purchased
for $189. How much does 1 ball cost and how much does 1 ball bag cost?

Found 2 solutions by checkley79, ankor@dixie-net.com:
Answer by checkley79(3341) (Show Source):
You can put this solution on YOUR website!
10X+Y=155 MULTIPLY BY -2 & ADD.
12X+2Y=189
-20X-2Y=-310
--------------------
-8X=-121
X=-121/-8
X=$15.125 COST OF ONE BALL.
10*15.125+Y=155
151.25+Y=155
Y=155-151.25
Y=$3.75 COST OF ONE BAG.
PROOF:
12*15.125+2*3.75=189
181.50+7.50=189
189=189

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
10 balls and 1 ball bag purchased for $155. 12 balls and 2 ball bags purchased
for $189. How much does 1 ball cost and how much does 1 ball bag cost?
let a = no. of balls
let b = no. of bags
:
"10 balls and 1 ball bag purchased for $155."
10a + b = 155
:
"12 balls and 2 ball bags purchased for $189"
12a + 2b = 189
:
How much does 1 ball cost and how much does 1 ball bag cost?
:
Multiply the first equation by 2, subtract the 2nd equation
20a + 2b = 310
12a + 2b = 189
------------------subtracting eliminates b, find a
8a = 121
a = 121/8
a = $15.125 for 1 ball.
:
Find the cost of the bag using the 1st original equation
10(15.125) + b = 155
151.25 + b = 155
b = 155 - 151.25
b = $3.75 for 1 bag
:
We expect the solution to be an even cents, check this in the 2nd equation
12(15.125) + 2(3.75) =
181.50 + 7.50 = 189; checks out with these values