Question 163066: A mosaic statue is 74 years older than an engraving. Thirty years ago, the mosaic was three times as old as the engraving. Find the present age of each.
Answer by joecbaseball(37)   (Show Source):
You can put this solution on YOUR website! For this, you just have to be able to make sense of what is written.
First, write an equation for the statement “A mosaic statue is 74 years older than an engraving.”
Let m be present age of the mosaic statue, and let e be present age of the engraving.
Then m = e + 74.
Now, don’t get confused by the wording. You have a second statement which you need to interpret. It says, “Thirty years ago, the mosaic was three times as old as the engraving.”
Your equation for this is m = 3e. Don’t worry about the “thirty years ago” part. Thirty years ago, the mosaic statue was still 74 years older than the engraving. Either that, or you can subtract 30 from the current ages of each. This would give you:
m – 30 = 3e – 30, which is the same as m = 3e.
So, now you have two equations with two unknowns. They are:
m = e + 74 and m = 3e.
Replace one of the m values in the other equation.
This gives 3e = e + 74. Now solve for e by subtracting an e from both sides:
This gives 2e = 74, and divide both sides by 2 to get e = 37.
Now substitute e = 37 into either of the equations:
m = e + 74….. m = 37 + 74….. Thus, m = 111
OR…
m = 3e……. m = 3(37)…… Thus, m = 111.
So…. The current ages are:
The mosaic is 111 years old and the engraving is 37 years old.
Good luck,
JoeC
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