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One integer is 8 less than another integer. The product of the lesser integer and -5 and 28 more than the greater integer. What are the integers?

One integer is 8 less than another integer. The product of the lesser integer and -5 and 28 more than the greater integer. What are the integers?

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Richard A. | Teaching runs in my familyTeaching runs in my family
4.9 4.9 (184 lesson ratings) (184)
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Hi George,
First, I suspect that the word and should be is. The product of the lesser and -5 is 28 more than the greater integer. In that case, the equation should be -5(N-8) = N + 28. In that case you can solve for N = 2 and N-8 = -6
James B. | Experienced, Patient, Passionate Math Tutor (In-person and online)Experienced, Patient, Passionate Math Tu...
5.0 5.0 (2393 lesson ratings) (2393)
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Let x = one integer (the lesser one)
Let x + 8 = the larger integer

The product of the lesser integer and -5 is -5x, That product is 28 more than the greater integer.
We can construct the following equation:

-5x = x+8 + 28
-5x = x + 36
-6x = 36
x = -6

The smaller integer is -6.
Since the greater number is 8 more than the lesser one, -6 + 8 = 2. The larger integer is 2.

CHECK:

2 - 8 = -6

-5(-6) = 2 + 28
36 = 26