문자와 식 전체 문제

Alejandra is driving to Cincinnati, Ohio, $450$ miles away. If she wants to be there in $6$ hours, at what rate does she need to drive?

Aisha took the train from Spokane to Seattle. The distance is $280$ miles, and the trip took $3.5$ hours. What was the speed of the train?

Philip got a ride with a friend from Denver to Las Vegas, a distance of $750$ miles. If the trip took $10$ hours, how fast was the friend driving?

Converting temperature While on a tour in Greece, Tatyana saw that the temperature was $40^\circ$ Celsius. Solve for $F$ in the formula $C=\frac{5}{9}(F-32)$ to find the temperature in Fahrenheit.

Converting temperature Yon was visiting the United States and he saw that the temperature in Seattle was $50^\circ$ Fahrenheit. Solve for $C$ in the formula $F=\frac{9}{5}C+32$ to find the temperature in Celsius.

The polynomial $-16{t}^{2}+300$ gives the height of an object $t$ seconds after it is dropped from a $300$ foot tall bridge. Find the height after $t=3$ seconds.

The polynomial $-8{t}^{2}+24t+4$ gives the height, in feet, of a ball $t$ seconds after it is tossed into the air, from an initial height of $4$ feet. Find the height after $t=3$ seconds.

The polynomial $-8{t}^{2}+24t+4$ gives the height, in feet, of a ball $x$ seconds after it is tossed into the air, from an initial height of $4$ feet. Find the height after $t=2$ seconds.

A window washer drops a squeegee from a platform $275$ feet high. The polynomial $-16{t}^{2}+275$ gives the height of the squeegee $t$ seconds after it was dropped. Find the height after $t=4$ seconds.

A manufacturer of microwave ovens has found that the revenue received from selling microwaves at a cost of p dollars each is given by the polynomial $-5{p}^{2}+350p.$ Find the revenue received when $p=50$ dollars.

Fuel Efficiency The fuel efficiency (in miles per gallon) of a bus going at a speed of $x$ miles per hour is given by the polynomial $-\frac{1}{160}{x}^{2}+\frac{1}{2}x.$ Find the fuel efficiency when $x=40\,\text{mph.}$

Stopping Distance The number of feet it takes for a car traveling at $x$ miles per hour to stop on dry, level concrete is given by the polynomial $0.06{x}^{2}+1.1x.$ Find the stopping distance when $x=60\,\text{mph.}$

Revenue A manufacturer of microwave ovens has found that the revenue received from selling microwaves a cost of $p$ dollars each is given by the polynomial $-5{p}^{2}+150p.$ Factor the greatest common factor from this polynomial.

Height of a baseball The height of a baseball hit with velocity $80$ feet/second at $4$ feet above ground level is $-16{t}^{2}+80t+4,$ with $t=$ the number of seconds since it was hit. Factor the greatest common factor from this polynomial.

A pair of glasses is dropped off a bridge $640$ feet above a river. The polynomial $-16{t}^{2}+640$ gives the height of the glasses $t$ seconds after they were dropped. Find the height of the glasses when $t=6.$

The fuel efficiency (in miles per gallon) of a bus going at a speed of $x$ miles per hour is given by the polynomial $-\frac{1}{160}{x}^{2}+\frac{1}{2}x.$ Find the fuel efficiency when $x=20$ mph.

A hiker drops a pebble from a bridge $240$ feet above a canyon. The polynomial $-16{t}^{2}+240$ gives the height of the pebble $t$ seconds a after it was dropped. Find the height when $t=3.$

The number of girls in a second-grade class is 4 less than the number of boys. Let b represent the number of boys. Write an expression for the number of girls.

Insurance copayment Carrie had to have 5 fillings done. Each filling cost $80. Her dental insurance required her to pay 20% of the cost as a copay. Calculate Carrie’s copay:

• ⓐ First, by multiplying 0.20 by 80 to find her copay for each filling and then multiplying your answer by 5 to find her total copay for 5 fillings.
• ⓑ Next, by multiplying 5(0.20)
• ⓒ Which of the properties of real numbers says that your answers to parts (a), where you multiplied 5[(0.20)(80)] and (b), where you multiplied 5(0.20), should be equal?

Cooking time Helen bought a 24-pound turkey for her family’s Thanksgiving dinner and wants to know what time to put the turkey in to the oven. She wants to allow 20 minutes per pound cooking time. Calculate the length of time needed to roast the turkey:

• ⓐ First, by multiplying $24\cdot 20$ to find the total number of minutes and then multiplying the answer by $\frac{1}{60}$ to convert minutes into hours.
• ⓑ Next, by multiplying $24\left(20\cdot \frac{1}{60}\right).$
• ⓒ Which of the properties of real numbers says that your answers to parts (a), where you multiplied $(24\cdot 20)\frac{1}{60},$ and (b), where you multiplied $24\left(20\cdot \frac{1}{60}\right),$ should be equal?