Ruby has 3 times as many two-rupee coins as she has five rupee-coins. If she has a total ₹88, how many coins does she have of each type?
Step-by-step solution
To find: The number of coins of each type
Idea: The ₹88 is the total value, not the number of coins. Value = (number of coins) × (value of each coin) for each type.
- Let the number of five-rupee coins be x. Then the number of two-rupee coins is 3x.½ mark
- Value of five-rupee coins = 5x; value of two-rupee coins = 2 × 3x = 6x.1 mark
- 5x + 6x = 88, so 11x = 88 and x = 8.1 mark
- Five-rupee coins: 8. Two-rupee coins: 3 × 8 = 24.½ mark
Check: 24 × ₹2 = ₹48 and 8 × ₹5 = ₹40; ₹48 + ₹40 = ₹88 ✓. And 24 = 3 × 8 ✓.
Answer to write in the exam
Let number of ₹5 coins = x; number of ₹2 coins = 3x
5x + 2(3x) = 88
11x = 88 ⇒ x = 8
∴ Ruby has 8 five-rupee coins and 24 two-rupee coins
Common mistakes that cost marks
- Writing x + 3x = 88. That adds numbers of coins, but 88 is the total value in rupees.
- Putting the 3 on the wrong coin: taking the five-rupee coins as 3x. The two-rupee coins are 3 times as many.
- Answering only x = 8 without stating how many of each coin.
How this can come in the exam
A purse has twice as many ₹10 notes as ₹20 notes, worth ₹320 in all. The number of ₹20 notes is
- 16
- 8
- 4
- 10
Show answer
(B) 8
20x + 10(2x) = 40x = 320, so x = 8.
A shop’s cash box has only ₹1 and ₹5 coins. There are 4 times as many ₹1 coins as ₹5 coins, and the coins are worth ₹180 in total.
(i) Taking the number of ₹5 coins as n, write the value of each type of coin. (ii) Form the equation. (iii) Find the number of each coin. (iv) How many coins are there altogether?
Show answer
(i) ₹5 coins: 5n; ₹1 coins: 4n × 1 = 4n (1 mark). (ii) 5n + 4n = 180 (1 mark). (iii) n = 20: 20 five-rupee and 80 one-rupee coins (1 mark). (iv) 100 coins (1 mark).Try one yourself
Kiran has 5 times as many ₹1 coins as ₹2 coins, worth ₹63 in all. How many of each?
Show answer
2x + 5x = 7x = 63, so x = 9: 9 two-rupee coins and 45 one-rupee coins.
More questions like this
- A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?
- If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?
- Observe the following growing pattern of square tiles.
Predict the number of squares in the next three stages of the pattern and write the sequence of numbers up to Stage 7 of the pattern. - This leads us to conclude that the number of squares at Stage n is given by 2n − 1.
Using the expression 2n − 1, can you find out how many tiles will be there in the 15th stage and the 26th stage of the pattern? Also, which stage will contain 21 tiles and 47 tiles? - Bela has ₹100 for pocket money. She spends ₹5 every day. After how many days will she be left with ₹40?