Ratios Real World Problems

[jenniferg]

How do I set up this problem?

Danny poured 78 liters of water into containers X, Y, and Z. The ratio of the volume of water in Container X to the volume of water in Container Y is 5:2. The ratio of the volume of water in Container Y to the volume of water in Container Z is 8:11. How much water was poured into Container X? How much more water was poured into Container X than Container Z?

I have gone through my textbook many times, but there is not an example like this one so I don't know what steps I need to take to set up/solve this problem. Any advice?

 

[Deleted member 4993]

How do I set up this problem?

Danny poured 78 liters of water into containers X, Y, and Z. The ratio of the volume of water in Container X to the volume of water in Container Y is 5:2. The ratio of the volume of water in Container Y to the volume of water in Container Z is 8:11. How much water was poured into Container X? How much more water was poured into Container X than Container Z?

I have gone through my textbook many times, but there is not an example like this one so I don't know what steps I need to take to set up/solve this problem. Any advice?

For all word problems- the first two steps are:

1) Name (assign variable name) to things you need to find.

Here you need to find:

Amount of water in container 'X' = X

Amount of water in container 'Y' = Y

Amount of water in container 'Z' = Z

2) Translate the given information to mathematical equations. What are the information given?

Danny poured 78 liters of water into containers X, Y, and Z → X + Y + Z = 78 ....................................(1)

The ratio of the volume of water in Container X to the volume
of water in Container Y is 5:2 → X/Y = 5/2 → 2X = 5Y → Y = 0.4 * X..............................................(2)

The ratio of the volume of water in Container Y to the volume
of water in Container Z is 8:11 → Y/Z = 8/11 → Z = 11/8 * Y → Z = 11/8 * 0.4 * X = 0.55 * X...........(3)

Use (2) and (3) in (1) and solve for X ...........................................................................................(4)

Use (4) in (3) and solve for Z