We will discuss here how to solve different types of word problems on dividing a quantity into three parts in a given ratio.
1. Divide $ 5405 among three children in the ratio 1\(\frac{1}{2}\)
: 2 : 1\(\frac{1}{5}\).
Solution:
Given ratio = 1\(\frac{1}{2}\) : 2 : 1\(\frac{1}{5}\)
= \(\frac{3}{2}\) : 2 : \(\frac{6}{5}\)
Now multiply each term by the L.C.M. of the denominators
= \(\frac{3}{2}\) × 10 : 2 × 10 : \(\frac{6}{5}\) × 10, [Since, L.C.M. of 2 and 5 = 10]
= 15 : 20 : 12
So, the amount received by three children are 15x, 20x and 12x.
15x + 20x + 12x = 5405
⟹ 47x = 5405
⟹ x = \(\frac{5405}{47}\)
Therefore, x = 115
Now,
15x = 15 × 115 = $ 1725
20x = 20 × 115 = $ 2300
12x = 12 × 115 = $ 1380
Therefore, amount received by three children are $ 1725, $ 2300 and $ 1380.
2. A certain sum of money is divided into three parts in the ratio 2 : 5 : 7. If the third part is $224, find the total amount, the first part and second part.
Solution:
Let the amounts be 2x, 5x and 7x
According to the problem,
7x = 224
⟹ x = \(\frac{224}{7}\)
Hence, x = 32
Therefore, 2x = 2 × 32 = 64 and 5x = 5 × 32 =160.
So, the first amount = $ 64 and the second amount = $ 160
Hence, total amount = First amount + Second amount + Third amount
= $ 64 + $ 160 + $ 224
= $ 448
3. A bag contains $ 60 of which some are 50 cent coins, some are $ 1 coins and the rest are $ 2 coins. The ratio of the number of respective coins is 8 : 6 : 5. Find the total number of coins in the bag.
Solution:
Let the number of coins be a, b and c respectively.
Then, a : b : c is equal to 8 : 6 : 5
Therefore, a = 8x, b = 6x, c = 5x
Therefore, the total sum = 8x × 50 cent + 6x × $ 1 + 5x × $ 2
= $ (8x × \(\frac{1}{2}\) + 6x × 1 + 5x × 2)
= $ (4x + 6x + 10x)
= $ 20x
Therefore, according to the problem,
$ 20x = $ 60
⟹ x = \(\frac{$ 60}{$ 20}\)
⟹ x = 3
Now, the number of 50 cent coins = 8x = 8 × 3 = 24
The number of $ 1 coins = 6x = 6 × 3 = 18
The number of $ 2 coins = 5x = 5 × 3 = 15
Therefore, the total number of coins = 24 + 18 + 15 = 57.
4. A bag contains $ 2, $ 5 and 50 cent coins in the ratio 8 : 7 : 9. The total amount is $ 555. Find the number of each denomination.
Solution:
Let the number of each denomination be 8x , 7x and 9x respectively.
The amount of $ 2 coins = 8x × 200 cents = 1600x cents
The amount of $ 5 coins = 7x × 500 cents = 3500x cents
The amount of 50 cent coins = 9x × 50 cents = 450x cents
The total amount given = 555 × 100 cents = 55500 cents
Therefore, 1600x + 3500x + 450x = 55500
⟹ 5550x = 55500
⟹ x = \(\frac{55500}{5550}\)
⟹ x = 10
Therefore, the number of $ 2 coins = 8 × 10 = 80
The number of $ 5 coins = 7 × 10 = 70
The number of 50 cent coins = 9 × 10 = 90
● Ratio and proportion
10th Grade Math
From Dividing a Quantity into Three Parts in a Given Ratio to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Sep 13, 24 02:48 AM
Sep 13, 24 02:23 AM
Sep 13, 24 01:20 AM
Sep 12, 24 03:07 PM
Sep 12, 24 02:09 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.