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?

5

1025

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? 3 n d 5 10 =525dn

5 10 523 = 5nn

35 =525n =15n

3 15 d

45 d

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

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

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???

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 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

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

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

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

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)

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

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

Assignment

Page 390 #1-16 all