Question

directions: write and solve an equation to solve each problem.

1. elijahs workout at the gym consists of just the elliptical and treadmill. after burning 450 calories on the elliptical machine, elijah switched to the treadmill. if he is burning 12.5 calories per minute on the treadmill, find the total number of calories he will have burned during his workout if he spends 30 minutes on the treadmill.
2. a candle that is 8 inches tall burns at a rate of ¾ inches per hour. find the height of the candle after 4 hours.
3. a car that was originally worth $29,500 depreciates at a rate of $2,500 per year. find the value of the car after six years.
4. for signing up for the rewards program at the pizzeria, haley got a card with 15 points. for each pizza she orders, she earns 8 points. once she hits 175 points, she gets a free pizza. how many pizzas will she need to order to get a free one?
5. an airplane at an altitude of 35,000 feet begins descending at a rate of 2,000 feet per minute. how long will it take the airplane to reach the ground?
6. the water level of a certain lake is at 35 feet. due to recent storms, the water level is rising at a rate of 3 inches per day. how many days will it take the lake to reach a level of 40 feet?

Explanation:

Problem 5

Step1: Calculate treadmill calories

Let $C_t$ = calories from treadmill.
$C_t = 12.5 \times 30$

Step2: Total burned calories

Let $C_{total}$ = total calories.
$C_{total} = 450 + C_t$
$C_{total} = 450 + (12.5 \times 30) = 450 + 375 = 825$

Problem 6

Step1: Calculate total burned length

Let $L_b$ = burned length.
$L_b = \frac{3}{4} \times 4$

Step2: Find remaining height

Let $H_f$ = final height.
$H_f = 8 - L_b$
$H_f = 8 - (\frac{3}{4} \times 4) = 8 - 3 = 5$

Problem 7

Step1: Calculate total depreciation

Let $D_t$ = total depreciation.
$D_t = 2500 \times 6$

Step2: Find final car value

Let $V_f$ = final value.
$V_f = 29500 - D_t$
$V_f = 29500 - (2500 \times 6) = 29500 - 15000 = 14500$

Problem 8

Step1: Points needed from orders

Let $P_n$ = needed points.
$P_n = 175 - 15$

Step2: Calculate number of pizzas

Let $N_p$ = number of pizzas.
$N_p = \frac{P_n}{8}$
$N_p = \frac{175 - 15}{8} = \frac{160}{8} = 20$

Problem 9

Step1: Set up time equation

Let $t$ = time in minutes.
$35000 = 2000t$

Step2: Solve for time

$t = \frac{35000}{2000} = 17.5$

Problem 10

Step1: Convert height to inches

Let $H_n$ = needed height gain.
$H_n = (40 - 35) \times 12 = 60$ inches

Step2: Calculate days needed

Let $d$ = number of days.
$d = \frac{60}{3} = 20$

Answer:

1. 825 calories
2. 5 inches
3. $\$14,500$
4. 20 pizzas
5. 17.5 minutes
6. 20 days