MPM2D – Problem Solving Test Review I
1. A football costs three times as much as a basketball. In one month, 41 basketballs and 13 footballs were sold for a total of $1244. What is the price of a football, and of a basketball? [$46.65, $15.55]
2. Ticket sales for a play amounted to $5760 for 800 tickets. Ticket prices were $5 and $10. How many tickets were sold for $10, and how many for $5? [352, 448]
3. A submarine cruises underwater at 10km/h and on the surface at 17km/h. The submarine travels a distance of 160km in 12.5h. How long did the sub travel underwater and how long on the surface?
[7.5h, 5h]
4. A jet travels to Winnipeg in 3 hours against the wind, but the return flight only takes 2.5 hours. If the distance to Winnepeg is 1500km, what is the speed of the plane in still air, and what is the speed of the wind? [550km/h, 50km/h]
5. How many kilograms of peanuts and cashews should be mixed together to make a mixture of 60kg to sell at $6. Peanuts sell for $4/kg and cashews sell for $12/kg. [45kg, 15kg]
6. A metallurgist has copper alloys, some of which contain 30% copper, and some with 48% copper. How many kilograms of each alloy should be mixed to make 240kg of an alloy with 36% copper?
[160kg, 80kg]
7. A sum of money was invested in 2 stocks. The first investment earned 8% interest, and the second earned 12%. The second investment earned twice as much as the first. The total amount of interest earned was $1440. How much was invested in each stock? [$6000, $8000]
8. The distance from Brampton to Peterborough is 240km. Greg is able to drive at an average speed of 100km/h along the 401 and 80km/h along Highway 115. If the total trip takes 2.5h, how long does Greg drive along Highway 115? [0.5h]
9. Solve for x and y:
[x = 12°, y = 17°]