R-A1 Honors Problem Solving Review for the Trimester 1 Final Exam Complete in
All problems need let statements, verbal sentences, equations, worked out solutions, and word answers.
1. A train left a station traveling 100 km/h. A second train left 2 hours later and headed in the same
direction at 125 km/h. After how many hours did the second train overtake the first train?
2. Adult tickets for the game cost $4 each and student tickets cost $2 each. A total of 920 tickets
worth $2446 were sold. How many student tickets were sold?
3. Kevin can put siding on a house in 30 hours. Alex can do the same job in 24 hours. How long would it
take if they both worked together?
4. The length of a green rug is 12 feet more than its width (w). A gold rug, which is 2 feet wider and 3
feet shorter than the green one, has a perimeter of 54 feet. Find the dimensions of the green rug.
Make a sketch of the rugs and label all dimensions.
5. In one game Monte scored twice as many points as Rick. In the next game Monte scored 6 fewer
points than he did in the first game, while Rick scored 9 more than he did in the first game. If they
both scored the same number of points in the second game, what were their scores in the first game?
6. At 7:45 a.m. Katie started filling her circular hot tub with water. At 8:21 a.m. there was 1 foot of
water in the tub. When will the hot tub have 2¼ feet of water in it? Write a direct variation
equation that shows the water depth, d, in terms of the minutes it’s been filling, m, and then use your
equation to answer the problem.
7. Rachel has $1.20 in only pennies and nickels. If she has exactly 36 coins in all find the number of
pennies and nickels that she has.
8. A rectangle is twice as long as it is wide. If its length is increased by 6 in. and its width is decreased
by 2 in., its area is increased by 12 in2. Find its original dimensions.
9. Reiko spent 4 h biking up Rich Mountain, rested for 30 min., and biked back in 3 hours. How far did
she bike in all if her rate of ascent was 1.5 km/h less than her rate of descent?
10. Devin has been renting an apartment for just over 5 years and his rent this year is $780. The rental
agreement he signed when he moved in stated that the rent will increase $70 each year. Write a
linear equation in slope-intercept form which gives the rent in terms of the number of years he’s lived there.
11. Hector Herrera made a rectangular fishpond surrounded by a brick walk 2 m wide. He had enough
bricks for the area of the walk to be 76 m2. Find the dimensions of the pond if it is twice as long as it
12. Elton bought stadium cushions for resale. He paid $5 for each cushion, and he sold all but 10
cushions for $12 each. His profit was $1000. How many cushions did he buy?
13. The difference of two integers is 7. Four times the smaller is 6 more than twice the larger. Find the
14. A motor home and a car traveled in opposite directions from the same starting point. The rate of the
car was 10 mph faster than the motor home. After 5 hours they were 600 miles apart. Find the
speed each was driving.
15. A grocer has peanuts selling for $1.50/lb. and raisins selling for $1.25/lb. He mixed how many pounds
of each to make a mixture of 10 pounds at $1.30/lb.?