A local charity is wrapping holiday gifts for local needy families. When 8 volunteers work together, they can get all of the gifts wrapped and distributed in 6 hours. How many hours would it have taken if there had been 12 volunteers, each working at the same rate?

*Since 8 volunteers take 6 hours to complete the wrapping and present distribution, a total of 8(6) = 48 “man-hours” were used. Knowing that 48 man-hours were required to complete the tasks, if 12 volunteers had been available, the tasks would have only taken 48/12 = ***4 ***hours to complete.*

Trent’s class wants to “adopt a family” from the local “angel tree.” The family they decide to adopt has asked for canned foods and a stuffed animal for their young daughter. If each student in the class each donates $5.00, they will have enough to buy 2 crates of canned food and will have exactly $1.00 left over. If each student brings in $8.00, they will have exactly enough to buy 3 crates of canned food and a stuffed animal that costs $11.50. How many students are in Trent’s class?

*Let’s call the number of students in Trent’s class c and the cost of the crates of food f. Now, we can set up the following equations:*

*2f + 1.00 = 5c*

*3f + 11.50 = 8c*

*Notice we have 2 equations and 2 variables. So, we can solve the system of equations. Here, we’ll use the elimination method:*

*2(3f + 11.50 = 8c) → 6f + 23.00 = 16c*

*3(2f + 1.00 = 5c) → 6f + 3.00 = 15c*

*Now, *

*6f + 23.00 = 16c*

*- (6f + 3.00 = 15c)*

*20 = c*

*So, there must be ***20 ***students in Trent’s class.*

Greta and Marge are collecting money for a local charity by taking donations outside of busy local businesses. Hoping to collect the most money today, Greta gets to her collection spot and begins collections at 8 a.m. Marge wanted to sleep in, so she didn’t start collections at her spot until 11 a.m., by which time Greta had already collected $45.00. If Greta continues to collect money at a rate of $15 per hour, Marge collects money at a rate of $20 per hour and they each take a 1-hour break at 2 p.m., at what time will Greta and Marge have collected the same amount of money?

*Let’s call the number of hours Greta and Marge are both collecting x. Now, we can set up the following equation:*

*45 + 15x = 20x*

*Now, solve for x:*

*45 = 5x (by subtracting 15x from both sides of the equation)*

*9 = x (by dividing by 9 on both sides of the equation)*

*So, once Marge starts collecting, they would have to continue for 9 hours to have collected the same amount that day – 9 hours after 11 a.m. is 8 p.m. However, since the two girls took an hour break at 2 p.m., that means they would have to collect until ***9*** p.m.*

**♦ Page 1 of the linked PDF contains PROBLEMS & SOLUTIONS.**

**Page 2 contains ONLY PROBLEMS. ♦**