8.6 Coin, Ticket, Weight, and Digit Problems

Pattern Set up two equations One equation is a physical amount that you can count with two different categories The other equation will have a dollar amount associated with it or a weight associated with the different categories to give a total dollar or pound amount.

Coin Problems

This coin equals how many pennies? Quarter Nickel Dime

A vending machine only takes nickels and dimes. There are three times as many dimes as nickels in the machine. The face value of the coins is $5.25. How many of each coin are in the machine? 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?

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? A jar of dimes and quarters contains $ There are 103 coins in all. How many of each are there? Try This Let q = the number of quarters Let d = the number of dimes -10 ( ) =

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? A jar of dimes and nickels contains $2.55. There are 30 coins in all. How many of each are there? Try This -5 ( ) =

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? A jar of quarters and nickels contains $3.00. There are 6 more nickels than quarters. How many of each are there? Try This 25 ( ) = Anyone get 11 quarters and 17 nickels???

Ticket Problem

There were 166 paid admissions to a game. The price was $2 for adults and $0.75 for children. The amount taken in was $ How many adults and children attended? A+ C =166 and 2A C = A = 166 –C 2(166-C) +0.75C = C +0.75C = C = C=31 A=135

Weight Problem

A jar contains 5 gram bolts and 10 gram bolts. The contents of the jar weigh 3.8 kg. If there are 460 bolts, how many of there of each kind? X = 5 gram bolts and y =10 gram bolts X +y = 460 and 5(x) + 10(y) =3800 You solve it X =160 5 gram bolts and y= gram bolts

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? 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. Try This =(?)

Vocabulary Sum of a two digit # Add the digits together Example (s): 23 is 2+3 Xy is x + y 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 = 20+3 = 2(10) = =3(10) +2 Xy is yx Xy= x(10) + y Yx = y(10 +x

Formulas Sum of Two Digits X +y = (the word problem will tell you what it equals) Reversed (10y + x) =(10x +y) ±(the word problem will tell you)

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 10. If the digits are reversed, the new number is 36 less than the original number. Find the original number. Try This 7337 x y

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 11. If the digits are reversed, the new number is 9 more than the original number. Find the original number. Try This 56

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? 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? Assignment Page 390 #1-16 all