Equations

Using a One-Step Equation as a Model Toucans and blue-and-yellow macaws are both tropical birds. The length of the average toucan is about 2 3 of the length of an average blue-and-yellow macaw. Toucans are about 24 inches long. Determine the length of an average blue-and-yellow macaw.

Using a One-Step Equation as a Model An online DVD company offers gift certificates that you can use to purchase rental plans. You have a gift certificate for $30. The plan you select costs $5 per month. Determine many months can you purchase with the gift certificate.

Using a One-Step Equation as a Model You have a rack that can hold 30 CDs. You can fit 7 more CDs on the rack before the rack is full. Determine many CDs are in the rack? Between 1788 and 2008, the U.S. Constitution was amended 27 times. Determine the amount years that have passed on average between one amendment and the next, to the nearest tenth of a year.

Two – Step Equation A delivery person uses a service elevator to bring boxes of book up to an office. The delivery person weights 160 pounds and each box of books weighs 50 pounds. The maximum capacity of an elevator is 1000 pounds. Determine the amount of boxes of books the delivery person bring up at one time.

Two – Step Equation Two college friends rent an apartment. They have to pay the landlord two month’s rent and a $500 security deposit when they sign the lease. To total amount they pay the landlord is $2800. Determine the rent for one month.

Using an Equation as a Model You are making a bulletin board to advertise community service opportunities in your town. You plan to use half a sheet of construction paper to each ad. You need 5 sheets of construction paper for a title banner. You have 18 sheets of construction paper. Determine the number of ads you can make. Suppose you need one quarter of a sheet of paper for each ad and four full sheets for the title banner. Determine the number of adds you can make now.

Multi – Step Equation You have a part time job. You work for 3 hours on Friday and 6 hours on Saturday. You also receive an allowance of $20 per week. You earn $92 per week. Find how much you earn per hour at your part-time job.

Multi-Step Equation A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with each ticket that costs $19 per ticket. The Web site charges a fee of $16 for the entire purchase. The family is charged a total of $1132. Find the number of tickets the family bought.

Solving a Multi-Step Equation Martha takes her niece and nephew to a concert. She buys t-shirts and bumper stickers for them. The bumper stickers costs $1 each. Martha’s niece wants 1 shirt and 4 bumper stickers, and her nephew wants 2 shirts but no bumper stickers. If Martha’s total is $67, determine the cost of one shirt.

Solving a Multi-Step Equation Noah and Kate are shopping for new guitar strings in a music store. Noah buys 2 packs of strings. Kate buys 2 packs of strings and a music book. The book costs $16. Their total cost is $72. Determine the price of one pack of strings.

Multi – Step Equation A hair dresser is deciding where to open her own studio. If the hair dresser chooses Location A, she will pay $1200 per month in rent and will charge $45 per haircut. If she chooses Location B, she will pay $1800 per month in rent and will charge $60 per haircut. Find the amount of haircuts she will have to give in one month to make the same profit at either location.

Multi – Step Equation An office manager spent $650 on a new energy – saving copier that will reduce the monthly electric bill for the office from $112 to $88. Find how many months the copier will pay for itself.

Using an Equation with Variables on Both Sides It takes a graphic designer 1.5 hours to make one page of a Web site. Using new software, the designer could complete each page in 1.25 hours, but it takes 8 hours to learn the software. Find the amount of web pages the designer would have to make in order to save time using the new software.

Paraphrasing

DECODE the question (paraphrase, translating mathematical language). Problem: A survey shows that 28% of 1,250 people surveyed prefer vanilla ice cream over chocolate or strawberry. Determine how many of the people surveyed prefer vanilla ice cream. Paraphrase: If there are 1,250 students and 28% of them prefer vanilla ice cream, I need to know what 28% of 1,250 is. I also need to know that the word of in this context means multiply. I can change 28% into a decimal or into a fraction.

Opportunity to practice paraphrasing Mrs. Jones requires all of her algebra students to purchase a binder to be used in the classroom. She allows the students to bring their own binders or to bring money so that she may purchase one for them. She has 128 algebra students in all, and 56% of them bought their own binders. The rest brought money for her to purchase their binders. Determine how many binders Mrs. Jones must purchase.

RADAR READ the entire question. Identify what the question is ASKING or what the final product should be. DECODE the question (paraphrase translating mathematical language). APPLY the decoded information. REVIEW and RESTATE the answer. Make sure your answer is reasonable!