Mrs Li bought some oranges. She gave 1/2 of them to her sister, 1/4 of the remainder to her neighbour, 3/5 of those left to her children and had 6 left in the end. How many oranges did Mrs Li buy? Explain your workings
Thank you so much for this awesome answer . It helped me alot . Thank u very much
If she had 6 left after giving 3/5 to her children, she had 6/(2/5) = 15 to start.
If she had 15 left after giving 1/4 to her neighbors, she had 15/(3/4) = 20 to start.
If she had 20 left after giving 1/2 to her sister, she had 20/(1/2) = 40 to start out with in the first place.
Check:
40 - 20 = 20
20 - 5 = 15
15 - 9 = 6
Everybody is happy.
Alternatively:
X - X/2 = X/2
X/2 - (X/2)(2/5) = 3X/8
3X/8 - (3X/8)(3/5) = 6X/40 = 6
6X = 240 or X = 40.
I dont get the working ...van you explain it again?
To find out how many oranges Mrs Li bought, we can work backwards from the information given. Let's break it down step by step:
Step 1: Mrs Li gave away 1/2 of the oranges to her sister.
This means that she had 1 - 1/2 = 1/2 of the oranges left.
Step 2: Next, she gave away 1/4 of the remaining oranges to her neighbor.
Since 1/2 * 1/4 = 1/8, Mrs Li had 1/8 of the original number of oranges left.
Step 3: She then gave 3/5 of the remaining oranges to her children.
Using the previous count of 1/8 * 3/5 = 3/40, this means that Mrs Li had 3/40 of the original number of oranges left after giving them to her children.
Step 4: Finally, she had 6 oranges left.
Knowing that 3/40 of the original number of oranges is equal to 6, we can set up the equation: (3/40)x = 6, where x represents the original number of oranges.
To solve this equation, we need to isolate x. We can do this by multiplying both sides of the equation by the reciprocal of 3/40, which is 40/3.
(40/3) * (3/40) * x = (40/3) * 6
x = 80
So, Mrs Li bought 80 oranges in total.
Explanation of working: We used working backwards to find the original number of oranges Mrs Li bought. We started with the information given, subtracted the quantities she gave away or kept at each step, and solved for the unknown using the equation in the end.