Distributing/Factoring
8 + 3m = 7 + 4m
m = 1
An animal shelter conducts an annual fundraising drive. The animal shelter must raise enough money to cover their annual rental of $2,500 and weekly expenses of $450. So far, the shelter has received a one-time donation of $125 and pledged donations of $680 per week. Write an inequality that can be used to find w, the number of weeks it can take the shelter to meet the goal.
680w + 125 (greater than/equal to) 450w + 2,500
Yolanda deposited $3,000 into an account that earns 4.5% simple annual interest. Calculate the interest Yolanda will earn after six years.
$810
12.9x + 10 = 34 + 9.9x
x = 8
Caroline receives $80 for her birthday and earns $10 each time she babysits. Addison has saved $70 and earns $12 each time she babysits. How many times must the girls babysit, x, so that Addison has at least as much money as Caroline?
12x + 70 (greater than/equal to) 10x + 80
Calculate the interest earned if $4,700 is deposited into an account that earns 3.25% simple interest for 7 years.
$1,069.25
1/3x - 5 = -3 + 1/6x
x = 12
Roger and Novak have a hot dog eating contest. After the first 2 minutes, Roger has consumed 8 hot dogs and Novak has consumed only 7 hot dogs. From that point, Roger eats 3 hot dogs each minute while Novak eats 4 hot dogs per minute. Write an inequality that will solve how many minutes, m, will Novak have eaten more hot dogs than Roger?
8 + 3m < 7 + 4m
Marcus deposited $3,000 into an account that earns 4.5% compounded interest, compounded monthly. Determine the total account balance after six years.
$3,927.91
At one point during the summer, Marsha has read 500 pages of her summer reading assignment, and Jan has read 460 pages. Marsha reads 20 pages per week for the remainder of the summer, and Jan reads 30 pages per week for the remainder of the summer. Write an equation and solve how many weeks, w, will it take before the girls have read the same number of pages?
500 + 20w = 460 + 30w
w= 40
Lila is looking into alarm systems for her home. Company A offers a plan that has an initial fee of $40 then charges $30 per month. Company B offers a plan that charges $50 per month. Write an inequality and solve for how many months, x, will Company A cost less than Company B?
40 + 30x < 50x
x > 2
$6,480 is deposited into an account that earns 5.5% compound interest, compounded semi-annually, for 5 years. Calculate the account balance after 5 years.
$8,499.50
Two containers have leaks. Container X begins with 80 ounces and leaks at a rate of 0.6 ounce per minute. Container Y begins with 100 ounces and leaks at a rate of 1 ounce per minute. Write an equations and solve how many minutes, n, before the containers have the same number of ounces.
80 - 0.6n = 100 - n
n = 50
Betsy considers changing her music download service. Her current service offers downloads at $0.99 each with a monthly fee of $4.95. Betsy receives an offer from another service that offers a monthly fee of $6.75 with downloads at $0.74 each. Write an inequality and solve for how many songs, n, will Betsy need to download for the new service to cost less than her current service.
0.99n + 4.95 > 0.74n + 6.75
8 songs
Calculate the interest earned if $6,480 is deposited into an account that earns 5.5% compound interest, compounded semi-annually, for 5 years. Round to the nearest cent.
$2,019.50