Agenda March 1

Homework 18 Alg book p. 365 # 1 - 8, 16

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Quiz Wed.

The sum of two numbers is 60.  Their difference is 14.  What are the two numbers?   Write a system of equations and solve by elimination.

DO NOW

37 and 23

x + y = 60x ­  y = 14

Suppose your community center sells total of 292 tickets for a basketball game. An adult ticket costs $3. A student ticket costs $1. The sponsors collect $470 in ticket sales. Write and solve a system to find the number of each type of ticket sold.

Step 1: Define your variables a = adult tickets s = student tickets

Step 2: Write your equations total tickets a + s = 292 Total sales 3a + 1s = 470

Step 3: Solve a + s = 292 a + s = 292

-(3a + s = 470) -3a - s = -470 -2a = -178 -2 -2 a = 89

Step 4: Substitute in original equation 89 + s = 292 -89 -89 s = 203

Step 5: Label your answer 89 adult tickets and 203 student tickets

Your class sells a total of 64 tickets to a play. A student ticket costs $1 and an adult ticket costs $2.50. Your class collects $109 in total ticket sales. How many adult tickets did you sell? How many student tickets did you sell?

Define:

Equations:

Label:

Suppose a model airplane club publishes a newsletter.  Expenses are $.90 for printing and mailing each copy, plus $600 total for research and writing.  The price of the newsletter is $1.50 per copy.  How many copies of the newsletter must the club sell to break even?

Define:  Let x = the number of copies               Let y = the amount of expenses and income.

Write:      y = 0.9x + 600                y = 1.5x

Solve:  1.5x = 0.9x + 600             0.6x = 600                  x = 1000

To break even, the model airplane club must sell 1000 copies.

Suppose an antique car club publishes a newsletter.  Expenses are $.35 for printing and mailing each copy plus $770 total for research and writing.  The price of the newsletter is $.55 per copy.  How many copies of the newsletter must the club sell to break even?

3850 copies

Suppose you have $28.00 in your bank account and start saving $18.25 every week. Your friend has $161.00 in his account and is withdrawing $15 every week. When will your account balances be the same?

4 weeks

A metal worker has some ingots of metal alloy that are 20% copper and others that are 60% copper.  How many kilograms of each type of ingot should the metal worker combine to create 80 kg of a 52% copper alloy?

Define:  Let g = the mass of the 20% alloy               Let h = the mass of the 60% alloy

Write:     g  +  h    = 80          0.2g + 0.6h = 0.52(80)

Solve for one variable:  g = 80 ­ h

Substitute:  0.2g + 0.6h = 0.52(80)                     0.2(80 ­ h) + 0.6h = 41.6                     16 ­ 0.2h + 0.6h = 41.6                      16 + 0.4h = 41.6

      0.4h = 25.6                                    h = 64

Substitute: g + 64 = 80                    g = 16

To make 80 kg of 52% alloy, you need 16 kg of 20% copper alloy and 64 kg of 60% alloy 

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