SOLUTION: One number is 10 more than a second number. If the product of the two numbers is 144, what are the two numbers?

Question 1187272: One number is 10 more than a second number. If the product of the two numbers is 144, what are the two numbers?
Found 3 solutions by ikleyn, Alan3354, MathTherapy:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

There are two pairs of such numbers.

One pair is   (8,18).     Another pair is   (-8,-18).
Write and solve the equation
x*(x+10) = 144

Reduce it to the standard quadratic form and then solve by factoring or using the quadratic formula.

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
One number is 10 more than a second number. If the product of the two numbers is 144, what are the two numbers?
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Try pairs of integer factors of 144: 2*72, 3*48, etc.
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To solve it algebraically,
x*(x+10) = 144
x^2 + 10x - 144 = 0
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Now, to factor it, you need to find 2 numbers that differ by 10 and have a product of 144.
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If they were not integers, you would have to use the quadratic equation or complete the square.
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eg:
One number is 10 more than a second number. If the product of the two numbers is 154, what are the two numbers?
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x^2 + 10x - 154 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=716 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 8.37908816025965, -18.3790881602597. Here's your graph:

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The solver always says it can be factored, but not necessarily with integers.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

One number is 10 more than a second number. If the product of the two numbers is 144, what are the two numbers?

Correct answer:
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