Digit Word Problems. Critical Thinking Skill: Explicitly assessing information and drawing conclusions. Digit and Mixture Problems per 7

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1 Digit Word Problems Critical Thinking Skill: Explicitly assessing information and drawing conclusions AutoSave 1

2 Digit Word Problems x: tens y: ones (units) "digits" x + y: "sum of the digits" 10x + y: "original number" 10y + x: "if the digits are reversed, the new number is..." 35 x: y: original #: reversed #: AutoSave 2

3 ex 1: The sum of the digits of a two digit number is 10. When the digits are reversed, the new number is 36 less than the original number. Find the original number. Steps: 1. translate equations 2. Find 3. Evaluate and solve 4. Put digits together as number 5. Sentence AutoSave 3

4 The sum of the digits of a two digit number is 5. If the digits are reversed, the new number is 27 more than the original number. Find the original number. AutoSave 4

5 A fork and a knife weigh 50g and 70g, respectively. If the set contains 20 knives and forks and weighs 1,220g, how many knives and forks are there? AutoSave 5

6 A collection of nickels and dimes is worth $3.95. There are 8 more dimes than nickels. How many of each are there? AutoSave 6

7 Digit and Mixture Word Problems Homework The sum of the digits of a two-digit number is 9. The number is equal to six times the ones digit. Find the number. x = ten's digit The VALUE of the number will be y = one's digit 10x + y Sum of the digits is 9 x + y = 9 "The number is equal to six times the one's digit" 10x + y = 6y NOW solve the system by LINEAR COMBINATION or SUBSTITUTION: x + y = 9 10x + y = 6y becomes 10x - 5y = 0 or 10x = 5y and then 2x = y 5 (x + y = 9) 5x + 5y = 45 x + 2x = 9 15x = 45 3x = x = 3 x = 3 and x + y = y = 9 y = 6 SO, the number is 36. AutoSave 7

8 The sum of the digits of a two-digit number is 11. The number is 59 more than the tens digit. Find the number. AutoSave 8

9 When the digits of a two-digit number are reversed, the new number is 36 more than the original number. The units digit of the original number is twice the tens digit. What it the original number? AutoSave 9

10 When the digits of a two-digit number are reversed, the new number is 54 less than the original number. The sum of the digits is 8. What it the original number? AutoSave 10

11 The sum of the digits of a two-digit number is one-third of the number. The units digit is 5 more than the tens digit. What is the number? AutoSave 11

12 The charge for admission to the Science Museum is $1.25 for adults and 50 for children. On a day when 830 people paid to visit the museum, the receipts were $655. Find the number of adults and the number of children who were admitted that day. AutoSave 12

13 Amelda s Shoe Store had a special close-out sale on shoes. Dress shoes were $9 a pair and casual shoes were $6 a pair. The Brohmer family spent $66 on shoes. If they spent $6 more on dress shoes than on casual shoes, how many pairs of each kind did they buy? AutoSave 13

14 Mr. Whacker cashed a check for $285 and asked the teller to give him only $5 and $10 bills. He received a total of 39 bills. How many of each denomination did he receive? AutoSave 14

15 Four cheeseburgers and three shakes cost a total of $8.00. Two shakes cost $1.30 more than one cheeseburger. What is the cost of a shake? What is the cost of a cheeseburger? AutoSave 15

16 Erica bought a bag of ground coffee and a bag of sugar at the grocery store, which cost her $ The coffee is $8 per pound and sugar is 80 per pound. If the weight of her purchases was 7 pounds, how much of each item did she buy? AutoSave 16