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8.6 Digit and Coin Problems. Goal: To use a system of equations to digit problems.

8.6 Digit and Coin Problems

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Goal: To use a system of equations to digit problems

- 1. Betty leaves her purse in a store at the mall and averages 36 mi/h on her way home to Glenville, 140 miles away. Honest Harry discovers her purse and starts after her one hour later. If he averages 48 mi/h, how long will it take him to catch Betty? Will he catch her before she reaches Glenville?
- 2. Fred leaves the corner of Maple Avenue and Front Street on his bicycle, and travels west at 14 km/h. Two hours later Celia leaves the same corner and walks east at 5 km/h. How many hours does it take for Fred and Celia to be 104 km apart?

91

73

19

37

- The sum of the digits of a two digit number is 10. If the digits are reversed, the new number is 36 less than the original number. Find the original number.

82

28

32 =(?) 82 - 36

Sum of a two digit #

If digits are reversed

Switch the tens and ones spot but we can’t have the variables being multiplied together. We need to turn it into an addition problem

Example (s):

23 is 32

23 = 20+3 = 2(10) +3

32 = 30 +2 =3(10) +2

Xy is yx

Xy= x(10) + y

Yx = y(10 +x

Add the digits together

Example (s):

- 23 is 2+3
- Xy is x + y

Sum of Two Digits

Reversed

(10y + x) =(10x +y) ±(the word problem will tell you)

- X +y = (the word problem will tell you what it equals)

- 1. Betty leaves her purse in a store at the mall and averages 36 mi/h on her way home to Glenville, 140 miles away. Honest Harry discovers her purse and starts after her one hour later. If he averages 48 mi/h, how long will it take him to catch Betty? Will he catch her before she reaches Glenville?
- 2. Fred leaves the corner of Maple Avenue and Front Street on his bicycle, and travels west at 14 km/h. Two hours later Celia leaves the same corner and walks east at 5 km/h. How many hours does it take for Fred and Celia to be 104 km apart?

y

x

73

37

- The sum of the digits of a two digit number is 10. If the digits are reversed, the new number is 36 less than the original number. Find the original number.

- 1. Betty leaves her purse in a store at the mall and averages 36 mi/h on her way home to Glenville, 140 miles away. Honest Harry discovers her purse and starts after her one hour later. If he averages 48 mi/h, how long will it take him to catch Betty? Will he catch her before she reaches Glenville?
- 2. Fred leaves the corner of Maple Avenue and Front Street on his bicycle, and travels west at 14 km/h. Two hours later Celia leaves the same corner and walks east at 5 km/h. How many hours does it take for Fred and Celia to be 104 km apart?

- The sum of the digits of a two digit number is 13. If the digits are reversed, the new number is 45 less than the original number. Find the original number.

94

- The sum of the digits of a two digit number is 11. If the digits are reversed, the new number is 9 more than the original number. Find the original number.

56

- 5. Julie and George can row at the same rate in still water. They leave Carston at the same time, Julie going upstream and George going downstream. Julie rows for two hours and arrives in Polton, 3 miles from Carston. George rows for three hours and arrives at Burnburg, 13.5 miles from Carston. Find the rate of the current and the rate each rows in still water.
- 6. Dr. White leaves home to drive to a convention. She is traveling at 55 mi/h. She is 10 mi from home when her husband realizes she has forgotten her briefcase. How fast will he have to drive to catch her in two hours?
- 7. It is 280 miles from Memphis to Birmingham. An express train left Memphis traveling toward Birmingham at 70 mi/h. Two hours earlier a freight train left Birmingham traveling toward Memphis on a parallel track. The speed of this train was 50 mi/h. How long was it before the two trains met?