Writing equations from real life situations

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. How many weeks, w, will it take before the girls have read the same number of pages?

• 500+ 30w = 460 + 2w

• 30+ 500w = 20 + 460w

• 20+ 500w = 30 + 460w

• 500+20w = 460 + 30w

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. Which equation could be used to find after how many minutes they both will have eaten the same amount of hot dogs?

• 8+3x=7-4x

• -8+3x=7+4x

• 8+3x=7+4x

• 8-3x=7+4x

• None of the above.

Which scenario could be represented by the inequality 40 + 30x < 50x?

• A fitness club offers two membership options. The first option has an initial fee of $50 and then charges $30 per month. The second option has no initial fee but charges $40 per month. After how many months, x, will the first option be a better value than the second?

• 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. After how many months, x, will Company A cost less than Company B?

• Regina purchases a new cell phone. Her first option is to purchase a plan that charges $40 per month, and she receives a phone for $30. The second plan charges $50 per month, and she receives the phone for free. After how many months, x, will the first option cost less than the second option?

• The local theater charges $40 for each set of 4 adult tickets, or patrons can purchase a membership to the theater for $50 and pay $30 for each set of 4 adult tickets. After how many performances, x, is a membership the better option?

Jinger makes soap to sell at craft fairs. The first bar of soap sells for $2, and each additional bar costs $1.25. The cost of making the soap is $0.95 per bar. Jinger pays $50 for renting a booth. How many bars of soap, b, will Jinger need to sell to at least break even?

• 2+1.25(b − 1) = 0.95b + 50

• 3.25b0.95b + 50

• 2+1.25(b − 1) ≥ 0.95b + 50

• 1.25 +2(b − 1) = 0.95b + 50