Building and Solving Equations – Part 1
Solve each of the following by representing them as equations. State any assumptions
Building and Solving Equations – Part 2, Easy
Solve each of the following by representing them as equations.
made.
1. A man and woman run for 10 seconds each, covering 170 𝑚𝑒𝑡𝑟𝑒𝑠 in total. If
1. A girl buys five cans of cola for 350 Yen. How much does each can cost?
the man runs 𝑥 𝑚𝑒𝑡𝑟𝑒𝑠, state the distance that the woman runs.
Equation:
If the man runs 75 𝑚𝑒𝑡𝑟𝑒𝑠, how far does the woman run?
Assumption:
2. At a store, a man buys a combination of 7 bottles of milk and juice. Juice
2. A boy buys two drinks and pays with a 500 Yen coin. He receives 180 Yen in
change. How much did each drink cost?
costs 100 Yen a bottle and milk costs 180 Yen a bottle. He spent ¥940. How
many of each did he buy?
Equation:
Assumption:
3. A man has a walk and then a jog and covers 31𝑘𝑚. He walks at 5𝑘𝑚/ℎ and
3. A man spends 100,000 Yen at Yamadadenki and is given two options as a prize. He
can get a rice-cooker and 18,000 Yen cashback or get three rice cookers
jogs at 8𝑘𝑚/ℎ. He spent 5 hours walking and jogging. How many hours did he
jog for and how many hours did he walk for?
and 2,000 Yen cashback. How much is the rice-cooker worth?
Equation:
Assumptions (there are two!):
4. A combination of 10 computers and printers are running at an office.
Computers cost ¥45 each per hour to run and printers cost ¥70 each per
4. A man wins a raffle and is given three options. He can either receive 3 boxes of
chocolates and 300 Yen, a cash prize of 3,000 Yen or two bottles of wine and 800
Yen. How much is each box of chocolates and bottle of wine worth?
Equation:
Assumptions:
hour. At the office, these 10 items in total cost ¥525 in power per hour. How
many computers and how many printers are running?
Building and Solving Equations – Part 2, Hard
Building and Solving Equations – Part 2, Hard
Solve each of the following my representing them as equations.
Solve each of the following my representing them as equations.
1. A man orders 5 coffees and 7 cakes for his family, costing 5100 Yen. He is
1. A man orders 5 coffees and 7 cakes for his family, costing 5100 Yen. He is
told that the cost of a coffee and a cake (together) is 840 Yen. How much
told that the cost of a coffee and a cake (together) is 840 Yen. How much
does each coffee cost and each cake cost?
does each coffee cost and each cake cost?
2. Each child is given sweets. I try to give the children 6 sweets each but I am 9
2. Each child is given sweets. I try to give the children 6 sweets each but I am 9
short. Instead, I then try to give the children 4 sweets each and I have 9 left
short. Instead, I then try to give the children 4 sweets each and I have 9 left
over. How many children are there and how many sweets?
over. How many children are there and how many sweets?
3. Some boys are given counters. I try to give each boy 3 counters but I am 10
3. Some boys are given counters. I try to give each boy 3 counters but I am 10
short. I then give the boys 2 counters and have 20 left over. How many boys
short. I then give the boys 2 counters and have 20 left over. How many boys
are there and how many counters?
are there and how many counters?
4. I prepare cups of tea for some guests visiting my house. I try to give each
4. I prepare cups of tea for some guests visiting my house. I try to give each
guest 3 cups of tea but I need another 6 cups. I then try to make 2 cups each
guest 3 cups of tea but I need another 6 cups. I then try to make 2 cups each
but I have 4 left over. How many guests are there and how many cups of tea
but I have 4 left over. How many guests are there and how many cups of tea
did I make?
did I make?