Question 1203133: An art collector has a porcelain vase that is 15 years old and a crystal vase that is 95 years old. In how many year will the crystal vase be three times as old as the porcelain vase will be than?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39627)   (Show Source):
Answer by ikleyn(52864)  (Show Source):
You can put this solution on YOUR website! .
An art collector has a porcelain vase that is 15 years old
and a crystal vase that is 95 years old.
In how many year will the crystal vase be three times as old
as the porcelain vase will be  then?
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Let x be the number of years to pass until the crystal vase be three times as old
as the porcelain vase will be then (so, x is the unknown value under the problem's question).
Write an equation as you read the problem
95 + x = 3*(15+x).
Simplify it and find x
95 + x = 45 + 3x
95 - 45 = 3x - x
50 = 2x
x = 50/2 = 25 years. ANSWER
CHECK. In 25 years, the age of the porcelain vase will be 15+25 = 40 years;
the age of the crystal vase will be 95+25 = 120 years;
120 = 3*40, so the answer is correct.
Solved.
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What you really need to learn from my solution, is " to write equation/equations as you read the problem ".
It is a key to your success and to your survival as a student solving word problems.
Answer by greenestamps(13206)  (Show Source):
You can put this solution on YOUR website!
Here is a very different way of setting up and solving the problem.
Let the ages of the two vases when the crystal vase is 3 times as old as the porcelain vase by 3x and x. Then the difference in age between the two vases is 3x-x = 2x.
But the difference in the ages of the two vases is (now and always) 95-15 = 80 years. So
2x = 80
x = 40
When the crystal vase is 3 times as old as the porcelain vase, the two vases will be 3x = 120 an x = 40 years old.
Since that current ages of the two vases are 95 and 15, that will be 25 years from now.
ANSWER: 25 years
Better than the method shown by the other tutors?
No, not necessarily. Some students might find it easier, some won't.
The actual work to find the answer is less with this method; but it takes a bit more work analyzing the problem and getting it set up for solving.
The point of my showing a different way to solve the problem is to encourage you to always be open to the possibility of doing things in different ways. People doing that is how the world progresses.
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