Sue,Martin and Lucy have £1180 in the bank shared between them in the ratio 16:23:20. Marvin takes out £100 and Lucy puts some money into the bank.Their total money is now in the ratio 8:9:12.How much more money Lucy put into the bank? Could somebody help me to find the correct answer,please?
Given:
S:M:L = 16:23:20
Total = £1180
Actual amounts for each
S:M:L = (£1180/(16+23+20)*(16:23:20)
=£(320:460:400)
Marvin takes out £100, and Lucy puts in £x, so new ratio
(8:9:12) = (320:360:400+x)
If we multiply the left-hand side by 40, we get
(320:360:480) which equals (320:360:400+x)
Can you figure out what x should be?
£80..Thank you.
Yes, that is correct.
To solve this problem, we'll start by finding the initial amounts of money each person has.
Step 1: Calculate the total parts in the initial ratio.
The initial ratio is 16:23:20. To get the total parts, we sum the numbers in the ratio: 16 + 23 + 20 = 59.
Step 2: Calculate the amount of money per part.
We divide the total amount of money (£1180) by the total parts (59) to find the value of each part: £1180 ÷ 59 = £20.
Step 3: Calculate each person’s initial amount of money.
To find each person's initial amount, we multiply their respective ratio part by the amount per part we found in step 2.
Sue: 16 parts × £20/part = £320
Martin: 23 parts × £20/part = £460
Lucy: 20 parts × £20/part = £400
So initially, Sue has £320, Martin has £460, and Lucy has £400.
Next, let's calculate their new amounts after Marvin takes out £100 and Lucy puts some money into the bank.
Step 4: Calculate the new total parts.
With Marvin taking out £100, the total amount will decrease to £1180 - £100 = £1080. The new ratio is 8:9:12.
To find the new total parts, we sum the numbers in the new ratio: 8 + 9 + 12 = 29.
Step 5: Calculate the new amount of money per part.
We divide the total amount of money (£1080) by the new total parts (29) to find the new value of each part: £1080 ÷ 29 = £37.24 (rounded to two decimal places).
Step 6: Calculate each person's new amount of money.
To find each person's new amount, we multiply their respective ratio part by the new amount per part.
Sue: 8 parts × £37.24/part = £297.92
Martin: 9 parts × £37.24/part = £335.16
Lucy: 12 parts × £37.24/part = £446.88
Comparing Lucy's new amount (£446.88) to her initial amount (£400), we can determine how much more money Lucy put into the bank:
Amount Lucy put into the bank = £446.88 - £400 = £46.88.
Therefore, Lucy put £46.88 more into the bank.