 ### The sum of two numbers is 12. One number is x. The other number is ______.

Experiment with the Pattern
See the Pattern
Solve an Equation
Uses for this Technique

1. Vocabulary: number, sum, total, solve Review words as needed. Return to this page. Review the idea of "A Number" as needed. Return to this page.

2. The sum of two numbers is 12.
Experiment with a situation in which the sum of two numbers is 12.

1st: You enter the 1st number. Enter negatives as "-x" rather than "- x."
2nd: Compute the other number mentally yourself.
3rd: Press the button in each row to display the other number.
4th: Look for a pattern: Find a method for computing the other number.

 1st Number Other Number Total 12 12 12 12 12

Before you continue with the page, express to yourself
how you arrived at each other number when the sum of two numbers is 12.

If you used subtraction, part 3 will explain your method.

3. If the sum of two numbers is 12 and the first number is x, the other numbers is 12 - x.

 1st number 2nd number sum Because: 1 11 12 12 - 1 2 10 12 12 - 2 6 6 12 12 - 6 4 8 12 12 - 4 x 12 - x 12 12 - x

4. If the sum of two numbers is 12 and the first number is x, the other numbers is 12 - x.

This time the expression is the result of solving an equation.

Suppose the sum of two numbers is 12.

Algebraically this is written as x + y = 12.

Solve for y:
x + y = 12
-x             -x
---------------
y = 12 - x

If the sum of two numbers is 12 and the first number is x,
the other numbers is 12 - x.

You can even check this answer.

x + y = 12
x + (12 - x) = 12
x + 12 - x = 12
12 = 12

5. Uses of this this technique Review the meanings of:
complement, complementary angles, supplement, supplementany angles
Review how to write code as a step in solving word problems.

Solve the problems below and check the answer after each problem.

 5a. The sum of two numbers is 12. If the smaller number is doubled and added to the larger number, the result is 16. Find the numbers. [Check answer.] 5b. An angle is three times the size of its complement. Find the angles. [Check answer.] 5a. There are 12 coins in a bank and the coins have a value of \$1.20. The are five more dimes than nickels and all the rest of the coins are quarters. Find how many dimes are in the bank. [Check answer.]                    © 01-6-3 www.mathnstuff.com/math/algebra/qb/otherno.htm

 5a. The sum of two numbers is 12. If the smaller number is doubled and added to the larger number, the result is 16. Find the numbers.         The sum of two numbers is 12. So, one number is x and the other is 12 - x.         If the smaller number is doubled and added to the larger number, the result is 16. 2(smaller) + (larger) = 16 2(x) + (12 - x) = 16 2x + 12 - x = 16 x + 12 = 16 x = 8 and 12 - x = 4   The numbers are 8 and 4.

 5b. An angle is three times the size of its complement. Find the angles.       So, one angle is x and the other is 90 - x.           An angle is three times the size of its complement. (angle) = 3(complement) (x) = 3(90 - x) x = 270 - 3x 4x = 270 4x/4 = 270/4 x = 67.7 so 90 - x = 22.5   The angles measure 22.5° and 67.5°.

 5c. There are 12 coins in a bank and the coins have a value of \$1.20. The are five more dimes than nickels and all the rest of the coins are quarters. Find how many dimes are in the bank. (nickels) + (dimes) + (quarters) = 12   (total value) = \$1.20   .05(nickels) + .10(dimes) + .25(quarters) = \$1.20   5(nickels) + 10(five more than nickels) + 25(quarters) = 120   5(x) + 10(5 + x) + 25(quarters) = 120   5(x) + 10(5 + x) + 25(the rest of the 12 coins) = 120   5(x) + 10(5 + x) + 25(12 - (x + 5 + x)) = 120 5(x) + 10(5 + x) + 25(12 - 2x - 5) = 120 5x + 50 + 10x + 25(12 - 2x - 5) = 120 15x + 50 + 25(7 - 2x) = 120 15x + 50 + 175 - 50x = 120 -35x + 225 = 120 -35x = -105 x=3   x=3, and x + 5 = 8, and 12 -(x + 5 + x) = 1 The are 3 nickels, 8 dimes, and one quarter.