2.3 Models and Applications

Hang borrowed $7,500 from her parents to pay her tuition. In five years, she paid them $1,500 interest in addition to the $7,500 she borrowed. What was the rate of simple interest?

Find a linear equation to solve for the following unknown quantities: One number exceeds another number by $17$ and their sum is $31.$ Find the two numbers.

Find a linear equation to solve for the following unknown quantities: One number is three more than twice another number. If the sum of the two numbers is $36 ,$ find the numbers.

Find a linear equation to model this real-world application: It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers. The company has monthly operating expenses of $350 for utilities and $3,300 for salaries. What are the company’s monthly expenses?

It takes Andrew 30 min to drive to work in the morning. He drives home using the same route, but it takes 10 min longer, and he averages 10 mi/h less than in the morning. How far does Andrew drive to work?

On Saturday morning, it took Jennifer 3.6 h to drive to her mother’s house for the weekend. On Sunday evening, due to heavy traffic, it took Jennifer 4 h to return home. Her speed was 5 mi/h slower on Sunday than on Saturday. What was her speed on Sunday?

Find the dimensions of a rectangle given that the perimeter is $110$ cm and the length is 1 cm more than twice the width.

The perimeter of a tablet of graph paper is 48 in. The length is $6$ in. more than the width. Find the area of the graph paper.

A game room has a perimeter of 70 ft. The length is five more than twice the width. How many ft² of new carpeting should be ordered?

Find the dimensions of a shipping box given that the length is twice the width, the height is $8$ inches, and the volume is 1,600 in.³.

To set up a model linear equation to fit real-world applications, what should always be the first step?

If the total amount of money you had to invest was $2,000 and you deposit $x$ amount in one investment, how can you represent the remaining amount?

If Bill was traveling $v$ mi/h, how would you represent Daemon’s speed if he was traveling 10 mi/h faster?

Use the information to find a linear algebraic equation model to use to answer the question being asked.

Beth and Ann are joking that their combined ages equal Sam’s age. If Beth is twice Ann’s age and Sam is 69 yr old, what are Beth and Ann’s ages?

Use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of $20 and charges of $.05/min for calls. Company B has a monthly fee of $5 and charges $.10/min for calls.

Find the model of the total cost of Company A’s plan, using $m$ for the minutes.

Use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of $20 and charges of $.05/min for calls. Company B has a monthly fee of $5 and charges $.10/min for calls.

Find out how many minutes of calling would make the two plans equal.

Use this scenario: A wireless carrier offers the following plans that a person is considering. The Family Plan: $90 monthly fee, unlimited talk and text on up to 8 lines, and data charges of $40 for each device for up to 2 GB of data per device. The Mobile Share Plan: $120 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $35 for each device up to a s…

Use this scenario: A wireless carrier offers the following plans that a person is considering. The Family Plan: $90 monthly fee, unlimited talk and text on up to 8 lines, and data charges of $40 for each device for up to 2 GB of data per device. The Mobile Share Plan: $120 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $35 for each device up to a s…

For exercises 17 and 18, use this scenario: A retired woman has $50,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%.

If we let $x$ be the amount the woman invests in the 15% bond, how much will she be able to invest in the CD?

For exercises 17 and 18, use this scenario: A retired woman has $50,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%.

Two planes fly in opposite directions. One travels 450 mi/h and the other 550 mi/h. How long will it take before they are 4,000 mi apart…

For exercises 17 and 18, use this scenario: A retired woman has $50,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%.

Fiora starts riding her bike at 20 mi/h. After a while, she slows down to 12 mi/h, and maintains that speed for the rest of the trip. Th…

For exercises 17 and 18, use this scenario: A retired woman has $50,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%.

Raúl has $20,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 8% interest and par…

Use this scenario: A truck rental agency offers two kinds of plans. Plan A charges $75/wk plus $.10/mi driven. Plan B charges $100/wk plus $.05/mi driven.

Write the model equation for the cost of renting a truck with plan B.

Use this scenario: A truck rental agency offers two kinds of plans. Plan A charges $75/wk plus $.10/mi driven. Plan B charges $100/wk plus $.05/mi driven.

If Tim knows he has to travel 300 mi, which plan should he choose?

Use the formula given to solve for the required value.

The formula $F = \frac{m v^{2}}{R}$ relates force $\left(F\right)$, velocity $\left(v\right)$, mass , and resistance $\left(m\right)$. Find $R$ when $m = 45 ,$ $v = 7 ,$ and $F = 245.$

Use the formula given to solve for the required value.

$S u m = \frac{1}{1 - r}$ is the formula for an infinite series sum. If the sum is 5, find $r .$

Solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

Use the formula from the previous question to find the width, $W ,$ of a rectangle whose length is 15 and whose perimeter is 58.

Solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

Use the formula from the previous question to find $f$ when $p = 8 \text{and}\textrm{ } q = 13.$

Solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

Use the formula from the previous question to find $m$ when the coordinates of the point are $\left(4 , 7\right)$ and $b = 12.$

Solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

Solve for h: $A = \frac{1}{2} h \left(b_{1} + b_{2}\right)$

Solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

Find the dimensions of an American football field. The length is 200 ft more than the width, and the perimeter is 1,040 ft. Find the length and width. Use the perimeter formula $P = 2 L + 2 W .$

Solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

Using the formula in the previous exercise, find the distance that Susan travels if she is moving at a rate of 60 mi/h for 6.75 h.

Solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

If the area model for a triangle is $A = \frac{1}{2} b h ,$ find the area of a triangle with a height of 16 in. and a base of 11 in.

Solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

Use the formula from the previous question to find the height to the nearest tenth of a triangle with a base of 15 and an area of 215.

Solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

Solve for h: $V = \pi r^{2} h$

Solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

Solve for r: $V = \pi r^{2} h$

Solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.

The formula for the circumference of a circle is $C = 2 \pi r .$ Find the circumference of a circle with a diameter of 12 in. (diameter = 2r). Use the symbol $\pi$ in your final answer.