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Simultaneous Equations Word Problems: Age, Quantity & Mixture Problems
Exercise
Solve each word problem using simultaneous equations.
- A father is 32 years older than his son. In 4 years, the father will be 3 times as old as his son. Find their current ages.
- A bag contains 50 coins, all either $1 or $2 coins. The total value is $82. How many of each coin are there?
- A solution contains 25% alcohol. How much pure alcohol must be added to 40 litres to make a 40% solution?
- A shop sells pens for $6 and pencils for $2. A student buys 20 items for $72. How many pens were bought?
- A man is 5 times as old as his daughter. In 10 years, the man will be 3 times as old as his daughter. Find their current ages.
- A chemist mixes 15% and 35% solutions to get 60 litres of 25% solution. How many litres of each are needed?
- A parking lot has 100 cars and motorcycles. There are 240 wheels in total. How many cars are there? (Assume cars have 4 wheels, motorcycles have 2.)
- A fruit seller has apples and oranges. Apples cost $4 each, oranges cost $3 each. If he sells 25 fruits for $90, how many apples were sold?
- A goldsmith mixes gold of 60% purity and 90% purity to get 200 g of 75% purity. How much of each is used?
- A mother is 3 times as old as her daughter. In 15 years, the mother will be 2 times as old as her daughter. Find their current ages.
Answer Key
1. Father 44, son 12
2. $1 coins: 18, $2 coins: 32
3. 10 L
4. 8 pens
5. Daughter 10, man 50
6. 15%: 30 L, 35%: 30 L
7. 20 cars
8. 15 apples
9. 60%: 100 g, 90%: 100 g
10. Mother 45, daughter 15