Age Problem
Roger is 4 years younger than Sam. In 10 years the sum of their age is 84. What are their current ages now?
Roger is 30 years old and Sam is 34 years old.
A plumber can fix 1 pipe in 4 hours. An apprentice takes 6 hours. If they work together for 1 hour, how much of the job is left?
7/12
A train leaves a station at 60 mph. A second train leaves the same station an hour later, traveling at 75 mph. How long until the second train catches up?
Second train catches up in 4 hours (after traveling 300 miles).
A small business tracks sales of two types of pens over two days.
● On Monday, they sold 3 blue pens and 5 red pens.
● On Tuesday, they sold 4 blue pens and 2 red pens.
Represent the data using matrices and find the total items sold over the two days.
They sold 7 of blue pens and 7 of red pens in total.
You need 10 liters of a 25% acid solution. You have a 10% and a 40% solution. How many liters of each should you mix?
mix 5L of each
Sophie is twice as old as her brother Max. In 5 years, the sum of their ages will be 55. How old are they now?
Max = 15, Sophie = 30
Marcus can paint a room by himself in 3 hours, Alex can paint the same room in 7 hours. If they work together, how long will it take them to paint the room?
2.1 hours
A train travels 60 mph for 2 hours, then slows to 40 mph for 1.5 hours. How far did it go total?
180 miles
A clothing store sells two types of items: T-shirts and Jackets. The prices for these items at two different stores are shown in the matrix below:
Prices (in dollars):
Store A: [ 15 50 ]
Store B: [ 18 45 ]
Each row represents a store, and the columns represent the prices of T-shirts and Jackets, respectively.
A customer wants to buy the following quantities:
[ 3 ]
[ 2 ]
That means the customer wants to buy 3 T-shirts and 2 Jackets.
Which store offers the cheaper total cost?
Store B
A cashier has 20 coins made up of nickels (5¢) and dimes (10¢). The total value is $1.55. How many nickels and how many dimes does the cashier have?
9 Nickels and 11 dimes
Talia is 2 years older than her brother Kai. Three years ago, the ratio of Talia’s age to Kai’s age was 3:2. What are their current ages?
Kai is 7 years old, Talia is 9 years old.
Carla can assemble a set of furniture in 5 hours. David can do the same job in 3 hours. If they start working together but Carla stops after 1 hour, how much longer will David need to finish?
1 hour and 24 minutes
Two trains leave the same station at the same time, traveling in opposite directions. One train travels 20 mph faster than the other. After 3 hours, they are 330 miles apart. Find the speed of each train.
Train A = 45 mph; Train B = 65 mph
A coffee shop tracks how much milk, espresso, and sugar (in units) are used per drink. It wants to calculate total ingredients used in a day.
Latte: 2 1 1
Cappuccino: 1 2 1
Mocha: 2 1 2
Drink Ingredient Matrix (units per drink):
50
40
30
200 units of milk, 160 of espresso, and 150 of sugar.
A tea merchant wants to create 25 kg of a special blend of tea that sells for $11/kg by mixing black tea costing $8/kg with oolong tea costing $13/kg. How many kilograms of each type of tea should be used to create the blend?
Black tea 10kg, Oolong tea 15 kg
The sum of the ages of Tue and his son is 50 years. Five years ago, the product of their ages was six times the father's age at that time. What are their current ages?
Father is 39 years old; Son is 11 years old
A pool is being filled by two pipes:
● Pipe A can fill the pool in 4 hours.
● Pipe B can fill the pool in x hours, where x>4
Both pipes are turned on at the same time. After 2 hours, a technician discovers that Pipe B is partially clogged, so it’s shut off. Pipe A continues alone and finishes filling the pool 1 hour later.
8 hours
A car starts driving at 60 km/h. Fifteen minutes later, a second car starts from rest and accelerates uniformly. It catches up exactly 45 minutes after it starts. Find the acceleration of the second car.
Approximately 213.33 km/h
There are two types of limited combination meals. Two restaurants have inventories shown in the first table. Find the revenue, cost, and profit of the meals for each restaurant.
Green Tea and Fries Coke and Nuggets
Restaurant 1 20 15
Restaurant 2 14 18
Revenue Store Cost Profit
Green Tea and Fries $21 $9 $12
Coke and Nuggets $29 $11 $15
The total revenue for meals for restaurant 1 is $855 and for restaurant 2 is $729
The total cost for meals for restaurant 1 is $345 and for restaurant 2 is $291
The total profit for meals for restaurant 1 is $465 and for restaurant 2 is $393
A chemist has a 20% salt solution and a 50% salt solution. How many liters of each should she mix to make 10 liters of a 35% salt solution?
5 liters of the 20% solution; 5 liters of the 50% solution
Emma is twice as old as her brother Jack. In 6 years, the sum of their ages will be 42. How old are they now?
Jack is 10 years old, and Emma is 20 years old.
Sarah can paint a room in 5 hours. Her brother can do it in 3 hours. How long will it take them to paint the room together?
1 hr 52.5 min
Two boats leave the same dock at the same time. One boat travels upstream at 12 km/h, while the other boat travels downstream at 18 km/h. If the river's current flows at 3 km/h, how long will it take before they are 90 km apart?
3 hours
A factory produces 2 products. Product A needs 2 units of steel and 3 of plastic. Product B needs 1 unit of steel and 4 of plastic. If the factory makes 50 of A and 60 of B, how many total units of steel and plastic are needed?
280 and 290
You have a 20% salt solution and a 50% salt solution. How many liters of each should you mix to get 10 liters of a 30% solution?
3.33 L (50%)