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8.6 Coin, Ticket, Weight, and Digit Problems
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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.
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Coin Problems
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This coin equals how many pennies?
5
1025
Quarter
Nickel
Dime
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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? 3 n d 5 10 =525dn
5 10 523 = 5nn
35 =525n =15n
3 15 d
45 d
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A jar of dimes and quarters contains $15.25. There are 103 coins in all. How many of each are there?
Try T
his
Let q = the number of quartersLet d = the number of dimes
103q d 25 10 1525dq
-10 ( ) =
103010 10q d
15 495q 33q
33 103d 70d
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A jar of dimes and nickels contains $2.55. There are 30 coins in all. How many of each are there?
Try T
his
30n d
5 10 255dn
-5 ( ) =
15 5 50dn
5 105d 21d
3021n
9n
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A jar of quarters and nickels contains $3.00. There are 6 more nickels than quarters. How many of each are there?
Try T
his
6n q 5 25 300qn
25 ( ) =
25 25 150n q
30 450n15n
15 6q
9q
15 6 q
Anyone get 11 quarters and 17 nickels???
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Ticket Problem
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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 2A + 0.75C =293.25
A = 166 –C
2(166-C) +0.75C =293.25
332- 2C +0.75C =293.25
-1.25 C = -38.75
C=31
A=135
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Weight Problem
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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
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Digit Problems
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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 T
his
82 28
32 =(?) 82 - 36
91 1973 37
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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 32
• 23 = 20+3 = 2(10) +3
• 32 = 30 +2 =3(10) +2
• Xy is yx
• Xy= x(10) + y
• Yx = y(10 +x
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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)
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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 T
his
10x y
73 37
10 10 36y x x y x y
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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 T
his
11x y 10 10 9y x x y 56
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Assignment
Page 390 #1-16 all