Question

George is making 8 gallons of TropicalTrip punch. He has already poured in1 gal of pineapple juice and 2-1 gal oforange juice. The only other ingredientis 7-Up. How much 7-Up does Georgeneed?gal

Answer 1

George needs to make 8 gallons of tropical trip punch and the ingredients are pineapple juice, orange juice, and 7-Up.

He has 1 3/4 gallons of pineapple juice

and 2 1/2 gallons of orange juice.

To determine how much he needs of 7-Up, the first step will be to add the gallons of pineapple juice and orange juice that he already has.

Step 1. We add:

`1(3)/(4)+2(1)/(2)`

To add these fractions, we add separately the whole numbers and the fractions:

`(1+2)+((3)/(4)+(1)/(2))`

Since 1+2 is 3:

`3+((3)/(4)+(1)/(2))`

And, to add the fractions, we use the following formula:

`(a)/(b)+(c)/(d)=(a* d+b* c)/(b* d)`

Applying this to the sum we have:

`3+(3*2+4*1)/(4*2)`

solving the operations:

`3+(6+4)/(8)`
`3+(10)/(8)`

And we simplify 10/8 first as 5/4:

`3+(5)/(4)`

and now we simplify 5/4 as 1 1/4:

`3+1(1)/(4)`

to complete the sum, we add 3+1 and get:

`4(1)/(4)`

Step 2: From step 1 we know that he already has 4 1/4 gallons, and he needs to complete with 7-Up the 8 gallons.

So now, to find the amount of 7-up that he needs, we subtract 4 1/4 to 8:

`8-4(1)/(4)`

To make this subtraction, it will be useful to have both numbers as a fraction:

`8=(32)/(4)`

and

`4(1)/(4)=(17)/(4)`

So the subtraction we have to make is:

`(32)/(4)-(17)/(4)`

Since both fractions have the same denominator, we just subtract the numerators:

`(32-17)/(4)=(15)/(4)`

And finally, we simplify 15/4 to 3 3/4: