Math Word Problems Demystified - A Self Teaching Guide

EVALUATION: Take 78 and reverse the digits to get 87. Subtract

87 
 78 ¼9. Hence, the sum of the digits 7þ8 is 15 and the difference of

the two numbers is 9.

EXAMPLE:The one’s digit of a two-digit number is twice the ten’s digit. The

sum of the digits of the number is 12. Find the number.

SOLUTION:

GOAL: You are being asked to find a two-digit number.

STRATEGY: Letx¼the ten’s digit and 2x¼the unit’s digit. If the sum of

the digits is 12, the equation isxþ 2 x¼12.

IMPLEMENTATION: Solve the equation:

xþ 2 x¼ 12

3 x¼ 12

x¼ 4

2 x¼ 2  4 ¼ 8

Hence the number is 48.

EVALUATION: The ten’s digit is 4 and the one’s digit is twice the ten’s digit

since 2 4 ¼8. The sum of the digits is 4þ 8 ¼12.

EXAMPLE:In a three-digit number, the one’s digit is three more than the

hundred’s digit, and the ten’s digit is one more than the hundred’s digit. If the

sum of the three digits is 10, find the number.

SOLUTION:

GOAL: You are being asked to find a three-digit number.

STRATEGY: Let x¼the hundred’s digit andxþ 1 ¼the ten’s digit and

xþ 3 ¼the one’s digit. Since the sum of the digits of the number is 10, the

equation isxþxþ 1 þxþ 3 ¼10.

100 LESSON 10 Solving Digit Problems