One number is seven more than 10 times the another number. If the two numbers are added, the result is 95. Find the smaller number.

Answer 1

First you set variables, let's do the following :

a = smaller number

b = larger number

Second, you make your equations based on your word statement

b = 10*a + 7

a + b = 95

Next, you usually solve for one of the variables, but the first equation already does that.

Next, you insert the solved variable into the other equation and solve. In this case, the 1st equation goes into the 2nd equation.

a + (10*a + 7) = 95

11*a + 7 = 95

11a = 95 - 7

11a = 88

a = 88/11

a = 8

This is your smaller variable! The problem is now solved.

Let's keep going, solve for the other variable and then check our work.

Plug the now known variable into one of the equations to solve for the other variable

a + b = 95

8 + b = 95

b = 95 - 8

b = 87

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Always check your work

b = 10*a + 7

87 = 10*8 + 7

87 = 87 CORRECT

a + b = 95

87 + 8 = 95

95 = 95 CORRECT