Ganesh R. answered • 05/25/15
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This process will seem a lot longer than it actually is, but only because I'm going to try to be as detailed as possible.
We have to first assign a variable to each unknown number: s=smaller number and g=greater number
Since there are 2 variables, we are going to need 2 equations that utilize both these variable in order to solve this problem. We come up with the equations using keywords from the word problem.
It's a little subtle, but the "is" in the first sentence implies "equals". Therefore we can read the sentence as "The greater number equals 1 more than twice the smaller number."
"Twice" the smaller number means multiplied by 2, and 1 "more" means add 1.
Putting all this information together, we obtain the equation: g = 2s + 1
We use this same process for the second sentence to find the second equation. It is a little tricker though so we'll take it step by step.
"Three times the greater" gives us 3g
"Five times the smaller" gives us 5s
The "exceeds" part tells us that 3g equals 10 more than 5s.
Putting this together gives us the second equation: 3g = 5s + 10
Now that we have the two equations, it simply a matter of substitution. We know from the first equation that g = 2s + 1, so we can sub that into the second equation. Doing so gives us: 3(2s + 1) = 5s + 10
Distributing gives us: 6s + 3 = 5s + 10
Simplifying and solving for s gives us: s = 7
Now that we know s, we can plug it into either equation. The first one is easier so we'll use that. Plugging in 7 for s gives us: g = 2(7) + 1 = 15
We get the final answer of s = 7 and g = 15. We can check to make sure this is right.
Twice 7 plus one gives us 15. And three times 15 gives us 45, which exceeds five times the smaller, 5 x 7 = 35, by ten.
David W.
05/25/15