8 6 Coin Ticket Weight and Digit Problems
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? Nickel 5 Dime 10 Quarter 25
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?
Try This A jar of dimes and quarters contains $15. 25. There are 103 coins in all. How many of each are there? Let q = the number of quarters Let d = the number of dimes -10 ( = )
Try This A jar of dimes and nickels contains $2. 55. There are 30 coins in all. How many of each are there? -5 ( )=
Try This A jar of quarters and nickels contains $3. 00. There are 6 more nickels than quarters. How many of each are there? 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 $293. 25. How many adults and children attended? A+ C =166 and 2 A + 0. 75 C =293. 25 A = 166 –C 2(166 -C) +0. 75 C =293. 25 332 - 2 C +0. 75 C =293. 25 -1. 25 C = -38. 75 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= 300 10 gram bolts
Digit Problems
Try This 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 91 73 19 37
Vocabulary Sum of a two digit # If digits are reversed Add the digits together Switch the tens and ones spot but we can’t have the variables being multiplied together. Example (s): We need to turn it into an addition problem • 23 is 2+3 Example (s): • Xy is x + y • 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
Formulas Sum of Two Digits • X +y = (the word problem will tell you what it equals) Reversed • (10 y + x) =(10 x +y) ±(the word problem will tell you)
Try This 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. 73 37 x y
Try This 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
Assignment Page 390 #1 -16 all
- Slides: 19