Why is the minimum number of oranges 18, not 17, in a 5:3:1 fruit ratio?

[tomtomtom1]

Hi all

I have a ratio problem which i was hoping someone could help with.

The question is this:-

Barry bough a box full of fruit. The contained some apples, oranges and lemons in the ratio 5:3:1. Given that there were more than 50 pieces of fruit in the box work out the minimum number of oranges in the box.

I do the following:-

5+3+1=9

(50/9)*3=16.666..

You cannot have 0.666 of an orange the answer is 17.

But this is wrong the answer is in fact 18 according to the answer sheet but WHY?

I know it has something to do with the statement "more than 50 pieces" but i cannot figure it out.

Can someone help

 

[Ray Vickson]

Hi all

I have a ratio problem which i was hoping someone could help with.

The question is this:-

Barry bough a box full of fruit. The contained some apples, oranges and lemons in the ratio 5:3:1. Given that there were more than 50 pieces of fruit in the box work out the minimum number of oranges in the box.

I do the following:-

5+3+1=9

(50/9)*3=16.666..

You cannot have 0.666 of an orange the answer is 17.

But this is wrong the answer is in fact 18 according to the answer sheet but WHY?

I know it has something to do with the statement "more than 50 pieces" but i cannot figure it out.

Can someone help

Assume there are N pieces of fruit altogether. How many pieces of each type would there be?

 

[mafagafo]

If you were to have 5 apples, 3 oranges and one lemon, you would have 9 fruit.
So, you can only have n * 9 fruits where n is a positive integer.
Can you work out the smallest value for n such that n * 9 > 50?
What does that tell you about the minimum number of oranges?

 

[HallsofIvy]

Another, more "algebraic" way to do this is to let "x" be the number of lemons. Then the number of oranges is 3x and the number of apples is 5x. The total number is x+ 3x+ 5x= 9x so the number of fruit must be a multiple of 9. The smallest multiple of 9 larger than 5 is (9)(6)= 54.

 

[tomtomtom1]

The answer is 6, so 6 * 3 = 18. got it thanks

 

[tomtomtom1]

Past Exam Questions on Ratio

Hi i found a past exam ratio questions on line and attempted to do them, i have attached my results, can anyone spot any mistakes?

Thanks

 

[mafagafo]

First, no the answer is not 6. The answer is 18. Try not to take x for the ANSWER whenever you solve for x.

Second, I think you should open another topic to place that PDF.

Third, question 17 is correct to me.