Question

In a fruit punch drink, the 3 ingredients are apple juice, orange juice and cranberry juice. If

1
4
of the drink is apple juice and
3
10
is orange juice then write the ratio of cranberry juice to apple juice to orange juice in its simplest form

Answer 1

orange : cranberry : apple : orange

9 : 5 : 6

Explanation:

Given the following ratios (fraction):

`(apple)/(total) =(1)/(4)`

`(orange)/(total) =(3)/(10)`

in order to add/subtract fractions, we have to ensure that the denominators are the same, we can see that for the denominators listed above, the least common multiple for 4 and 10 = 20, hence we can re-write the above as :

`(apple)/(total) =(1)/(4) =(5)/(20)`

`(orange)/(total) =(3)/(10) =(6)/(20)`

Hence,

Fraction of cranberry juice of the total is,

1 -
`(5)/(20)` -
`(6)/(20)`

=
`(20)/(20)` -
`(5)/(20)` -
`(6)/(20)`

=
`(9)/(20)`

Because all the denominators are the same, we can assemble the ratios of each component by taking the ratios of the numerators

cranberry : apple : orange

= ratios of their numerators

= 9 : 5 : 6