Age Problem
Sarah is currently 3 times as old as her daughter Emma. In 12 years, Sarah will be only twice as old as Emma. How old are Sarah and Emma now?
Emma is 12 years old, Sarah is 36 years old
Maria can paint a fence in 4 hours, while her brother can paint the same fence in 6 hours. How long will it take them to paint the fence working together?
2.4 hours
Two cars leave the same city traveling in opposite directions. One travels at 60 mph and the other at 70 mph. How long until they are 390 miles apart?
t = 3 hours
A store sells apples for $2/lb and oranges for $3/lb. In January, they sold 100 lbs of apples and 150 lbs of oranges. In February, they sold 120 lbs of apples and 200 lbs of oranges. Use matrices to find total revenue for each month.
January: $650, February: $840
A chemist needs 100 mL of a 15% acid solution. She has a 10% solution and a 25% solution available. How much of each should she mix?
x = 66.67 mL, y = 33.33 mL
A mother is 3 times as old as her daughter. In 6 years, the sum of their ages will be 72. How old are they now?
The daughter is 15 years old The mother is 45 years old
Ella can paint a room by herself in 6 hours. Her friend Mia can paint the same room in 4 hours. If they work together, how long will it take them to paint the room?
It will take 2.4 hours, or 2 hours and 24 minutes, for Ella and Mia to paint the room together.
A train leaves City X heading toward City Y at 70 miles per hour.
Two hours later, a second train leaves City X on the same track, heading toward City Y at 90 miles per hour.
How long will it take the second train to catch up to the first train?
It will take 7 hours for the second train to catch up after it leaves.
A school is organizing a fundraiser and is selling two types of tickets: student tickets and adult tickets.
● On Day 1, the school sold 40 student tickets and 20 adult tickets for a total of $520.
● On Day 2, they sold 25 student tickets and 30 adult tickets for a total of $575.
Find the price of each type of ticket using matrices.
Student ticket price: $5.86
Adult ticket price: $14.29
A chemist wants to mix a 10% acid solution with a 30% acid solution to make 40 liters of a 20% solution. How many liters of each should be used?
20 liters of 10% solution; 20 liters of 30% solution
Annie, Bert, and Chris are three individuals with the following conditions:
1. The sum of their ages is 60 years.
2. Annie is older than Bert by the same number of years that Bert is older than Chris.
3. When Bert reaches Annie's current age, Annie will be three times as old as Chris is now.
• Annie is 28 years old
• Bert is 20 years old
• Chris is 12 years old
Jane, Paul, and Peter can finish painting a fence in 2 hours. If Jane can do it alone in 5 hours and Paul in 6 hours, how long would it take Peter to paint the fence alone?
It takes Peter 7.5 hours to paint the fence alone
A train travels 240 miles in the same time a car travels 180 miles. If the train travels 20 mph faster than the car, what is the speed of each?
Car speed = 60 mph; Train speed = 80 mph
A coffee shop sells small and large cups of coffee. On Monday, 3 small and 2 large coffees cost $13. On Tuesday, 4 small and 3 large cost $18. Find the price of each size.
Small coffee = $3; Large coffee = $2
A chemist needs 30 liters of a 20% acid solution for an experiment. She has:
● A 10% acid solution
● A 50% acid solution
How many liters of each solution should she mix to get exactly 30 liters of a 20% acid solution?
● Mix 22.5 liters of the 10% solution
● Mix 7.5 liters of the 50% solution
Ryson is twice as old as his son Sean. In 5 years, the sum of their ages will be 64. How old are Ryson and Sean now?
Ryson is 36 years old; Sean is 18 years old
John can fill the pool in 48 hours, and Lee can clear the pool in 55 hours. How long can they fill the pool?
If they both work at the same time they need 377.14 hours to fill up the pool
Daddy rows a boat, when he is downstream his speed is 6 miles per hour, and upstream is 4 miles per hour. As we know that his total hour for a river’s round trip is 10 hours, so how long is the river.
The river is 24 miles long.
A. x+2y+3z=0,
B. 2x+y+3z=6,
C. x-y=6,
D. x-2y-z=8
a= 1, b = 4, c = 1, d = -2
There are two cups of water solution, one solution has 20% of salt in it, and the other one has 5% of salt in it. When we mix both solutions into a big container and do not split them out, the solution in the container is 9% of salt water with a total mass of 300 grams. So, what is the total mass of 20% salt water?
20% salt water solution has 80g of mass