Solving Worded Problems – Easy
Solve the following with the use of equations. Assume each unknown (value,
weight, amount) has equal value.
Solving Worded Problems – Hard
Solve the following with the use of equations. Assume each unknown (value,
weight, amount) has equal value.
1. Jayne buys four chocolate bars for 500 Yen. Show how much each
chocolate bar is worth.
1. Miu buys 12 tickets at the amusement park and pays with 50,000 Yen.
She receives 2,000 Yen back in change. How much did each ticket cost?
2. A cat eats four mice and gains a total of 320 calories of energy. Show how
many calories each mouse represents.
2. Yuta queues up for three roller coaster rides and rides them, this takes
120 minutes. The total amount of time he had to queue up for was 114
minutes. How long was he on each ride?
3. Riho buys a drink and pays with 200 Yen. She gets 70 Yen back in change.
Show how much the drink cost her.
3. Kei decided to drink 142 cups of tea and spent 9 hours and 28 minutes
drinking them. How long did it take him to drink each cup on average?
4. A rat eats three kittens at a total weight of 1260g. Show how heavy each
kitten was.
5. Takafumi dyes his hair 4 times and altogether uses 120ml of dye. Show
how much dye he used each time.
6. Jungle Sena divides 24 spiders into 6 jars. Show algebraically how many
are in each jar.
7. Four balloons contain 7.2 litres of uncompressed air. Show algebraically
how much air is in each balloon.
4. A man trades four ornaments with another man who offers him two
different ornaments and 5,200 Yen. If each ornament has the same value,
how much is each ornament worth?
5. Ryusuke goes to the shop and buys 2 packs of strawberries for 240 Yen.
How much is each pack of strawberry worth?
Each pack of strawberries contains 15 strawberries. How much is each
strawberry worth?
Solving Simultaneous Worded Problems – Easy
Solve the following with the use of simultaneous equations. Assume each
unknown (value, weight, amount) has equal value.
1. Mayu buys three sweets and a toy for 110 Yen. Eri buys five sweets and
three toys for 250 Yen. How much does each sweet and toy cost?
Solving Simultaneous Worded Problems – Hard
Solve the following with the use of simultaneous equations. Assume each
unknown (value, weight, amount) has equal value.
1. A rectangle has area 48cm2 and perimeter 32cm. Write an expression for
each in terms of length and width.
Calculate the length and width.
2. Koshi buys five pairs of shoes and a hat for 32,000 Yen. Koz Kondo buys
two pairs of shoes and two hats for 16,000 Yen. How much do each cost?
3. Shiina goes to the beach twice and to Tokyo four times from Ota (each
time). He pays 18,000 Yen altogether. Ken goes to the beach once and to
Tokyo three times from Ota and pays 11,000 Yen. How much does a
round trip cost to each destination?
4. A number 𝑥 multiplied by 4 and then added to y makes 11. The number 𝑥
multiplied by 3 and added to 5y makes 1. Find each number.
5. A cat and two dogs weigh a total of 17kg. Two cats and five dogs weigh a
total of 40kg. The cats all weigh the same amount. The dogs also weigh
the same as each other. Find the weight of each.
2. A man walked for 3𝑥 miles and it took him 4y hours. He walked at 3mph.
The next day, he walks for 6𝑥 miles and it takes him 6y hours. He walks at
4mph now. Represent this information as a pair of simultaneous
equations. (Hint: Speed = Distance ÷ Time.)
Calculate 𝑥 and y.
How long did he walk for on both days in total? How much time did he
walk for on both days in total?
3. At a small amusement park, the entry fee for children is 150 Yen and the
entry fee for adults is 400 Yen. On one day, 2200 people enter the park
and the park makes 505,000 Yen. How many children entered the park
and how many adults entered?