SOLUTION: Dear Tutor, I need help with Problem Solving : one or More Numbers. The problem is the following: A Brand X bottle contains one dozen fewer capsules than a Brand Y bottle. Five

Click here to see ALL problems on Expressions-with-variables

Question 10389: Dear Tutor,
I need help with Problem Solving : one or More Numbers. The problem is the following:
A Brand X bottle contains one dozen fewer capsules than a Brand Y bottle. Five Brand X and 8 Brand Y bottles contain 486 capsules. How many capsules are in a Brand X bottle.
Please show the steps to this problem. Also I need this by Sunday September 11, 2005. Thank you.
Answer by prince_abubu(198) (Show Source):
You can put this solution on YOUR website!
Let's decipher the first sentence: "Brand X bottle contains 1 dozen fewer capsules than the Brand Y bottle". This is saying that brand X has less capsules in it than brand Y. It is VERY important to FIRST DETERMINE which one has more content. In this case, the Y contains more. If Y contains more, then it's the bottle that has to be knocked down by 12 capsules to equal the (fewer) number of capsules in bottle X. Our equation then is .

They then told us that 5 brand X bottles and 8 brand Y bottles have a total of 486 capsules. SO, 5 bottles * X capsules per bottle would give us the number of X-type capsules. Also, 8 bottles * Y capsules per bottle would give us the number of Y-type capsules. We need to total up the number of X and Y capsules to equal 486: .

Since we know about how many capsules of X there are in one bottle compared to how many capsules of Y there are in that bottle, we need to make a substitution. Since , we can substitute for the X in the equation .

<------- Notice that we placed parentheses around the Y-12. It's ALWAYS a good practice to place parentheses around what you substituted. We substituted so that the equation will only be in 1 variable. This way, you can solve the equation.

<----- distributed

<-------- combine like terms

<----- Add 60 to both sides

<------ There are 42 capsules in the Y-brand bottle. The problem does ask for how many X-capsules are in one bottle. Since We know that there are 12 less X-capsules in one bottle than there are Y-capsules, then there would be 30 capsules in the X-bottle. We actually plugged in the 42 in the equation to get the x. .