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?
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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
*[invoke solve_quadratic_equation 1,10,-154]
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The solver always says it can be factored, but not necessarily with integers.