Slope-Intercept Form (Sec

Problem Solving using Systems (Sec. 4.5)

Reminder: Steps for Problem Solving

1. UNDERSTAND the problem. Set variables for the unknown.

1. TRANSLATE the problem into an equation.

1. SOLVE the equation.

4. INTERPRET the results. Check your solution to see if it will work.

Finding Numbers

Example 1: A first number is 4 less than a second number. Four times the first number is 6 more than twice the second. Find the numbers.

Your Turn: A first number is 7 greater than a second number. Twice the first number is 4 more than three times the second. Find the numbers.

Solving Problems about Prices

Example 2: Angela goes to the store and buys 15 pens and 8 spiral notebooks for $12.95 (excluding taxes). Max buys 7 pens and 5 spiral notebooks for $7.50. How much does each pen cost? How much does each spiral cost?

Example 3: Cara is selling tickets for her high school play. She is selling adult tickets for $7 each and student tickets for $3 each. If Cara sells a total of 157 tickets for $723, how many of each type of ticket did she sell?

YOUR TURN: Eric goes to the store and buys 5 candy bars and 8 packs of gum for $10.85. He goes back two weeks later and buys 3 candy bars and 5 packs of gum for $6.70. How much does each candy bar cost? How much does each pack of gum cost?

Mixing Solutions

Example 4: Lynn Pike, a pharmacist, needs 70 liters of a 50% alcohol solution. She has available a 30% alcohol solution and an 80% alcohol solution. How many liters of each solution should she mix to obtain 70 liters of a 50% alcohol solution?

Example 5: One solution contains 20% acid and a second solution contains 50% acid. How many ounces of each solution should be mixed in order to have 60 ounces of a 30% acid solution?

Your Turn: The pharmacist needs 50 liters of a 35% alcohol solution. He has available a 20% alcohol solution and a 45% alcohol solution. How many liters of each does he need to mix in order to obtain the 50 liters of 35% alcohol solution?

Finding a Break-Even Point

Revenue:

Cost:

Break-Even Point:

Fixed cost:

Variable cost:

Example 4: A manufacturing company recently purchased $3,000 worth of new equipment to offer new personalized stationery to its customers. The cost of producing a package of personalized stationery is $3.00, and it is sold for $5.50. Find the number of packages that must be sold for the company to break even.

Example 5: A manufacturer sells a product for $10 per unit. The manufacturers fixed costs are $1200 a month, and the variable costs are $2.50 per unit. How many units must the manufacture produce each month to break even?

Your Turn: A company that manufactures boxes recently purchased $2,000 worth of new equipment to make gift boxes to sell to its customers. The cost of producing a package of gift boxes is $1.50 and it is sold for $4.00. Find the number of packages that must be sold for the company to break even.

Finding Angle Measurements

Example 6: The measure of the largest angle of a triangle is 80º more than the measure of the smallest angle, and the measure of the remaining angle is 10º more than the measure of the smallest angle. Find the measure of each angle.

Your Turn: The measure of the largest angle of a triangle is 40º more than the measure of the smallest angle, and the measure of the remaining angle is 20º more than the measure of the smallest angle. Find the measure of each angle.

Example 7: The sum of three numbers is 131. One number is six more than the smallest number. The remaining number is three times the smallest number. Find each number.

Your Turn: The sum of three numbers is 168. One number is eight more than the smallest number. The largest number is twice as much as the smallest number. Fine each number.

Example 8: In the 2000 Summer Olympics in Sydney, Australia, the U.S. earned 14 more gold medals than silver. The number of bronze medals earned was 17 less than twice the number of silver medals. The U.S. earned a total of 97 medals. How many of each kind of medal did the U.S. earn?