Can someone help me plz with this word problem.
Tanner is making her family's secret recipe of fruit punch for the barbecue this weekend. The ratios for mixing the perfect fruit punch is very specific so she pays special attention to the amounts and units. She combines 2 gallons of orange juice, 6 quarts of cranberry juice, 10 pints of apple juice, and 16 ounces of lemon juice. Find the following ratios in simplest form.
Orange juice to apple juice
Cranberry juice to apple juice
Apple juice to lemon juice
Cranberry juice to orange juice
Lemon juice to orange juice
well 16/10 = 8/5 I suppose :)
(In simple terms)
To find the ratios, we need to convert all the measurements to a common unit.
1 gallon = 4 quarts
1 quart = 2 pints
Given:
Orange juice = 2 gallons
Cranberry juice = 6 quarts
Apple juice = 10 pints
Lemon juice = 16 ounces
Converting the units:
Orange juice = 2 * 4 quarts = 8 quarts
Cranberry juice = 6 quarts
Apple juice = 10 * 2 pints = 20 pints
Lemon juice = 16 ounces
Now, let's calculate the ratios:
Orange juice to apple juice:
Ratio = Orange juice / Apple juice = 8 quarts / 20 pints
To simplify this ratio, we need to convert either quarts to pints or pints to quarts. Since 1 pint = 0.5 quarts, we'll convert the pints to quarts:
Ratio = 8 quarts / (20 pints * 0.5 quarts/pint)
= 8 quarts / 10 quarts
= 4/5
Therefore, the ratio of Orange juice to apple juice is 4/5.
Cranberry juice to apple juice:
Ratio = Cranberry juice / Apple juice = 6 quarts / 20 pints
Converting pints to quarts:
Ratio = 6 quarts / (20 pints * 0.5 quarts/pint)
= 6 quarts / 10 quarts
= 3/5
Therefore, the ratio of Cranberry juice to apple juice is 3/5.
Apple juice to lemon juice:
Ratio = Apple juice / Lemon juice = 20 pints / 16 ounces
Converting pints to ounces:
Ratio = (20 pints * 16 ounces/quart) / 16 ounces
= 320 ounces / 16 ounces
= 320/16
= 20
Therefore, the ratio of Apple juice to lemon juice is 20.
Cranberry juice to orange juice:
Ratio = Cranberry juice / Orange juice = 6 quarts / 8 quarts
Simplifying the ratio:
Ratio = 6/8
= 3/4
Therefore, the ratio of Cranberry juice to Orange juice is 3/4.
Lemon juice to orange juice:
Ratio = Lemon juice / Orange juice = 16 ounces / 8 quarts
Converting ounces to quarts:
Ratio = (16 ounces * 1 quart/32 ounces) / 8 quarts
= 0.5 quarts / 8 quarts
= 0.5/8
= 1/16
Therefore, the ratio of Lemon juice to orange juice is 1/16.
Sure, I can help you with that!
To find the ratios, we need to compare the quantities of different ingredients in terms of a common unit. In this case, we can convert all the measurements to ounces, since it's the smallest unit mentioned.
First, let's convert the measurements to ounces:
- 2 gallons of orange juice = 2 * 128 = 256 ounces
- 6 quarts of cranberry juice = 6 * 32 = 192 ounces
- 10 pints of apple juice = 10 * 16 = 160 ounces
- 16 ounces of lemon juice = 16 ounces
Now let's find the ratios in simplest form:
Orange juice to apple juice:
- Orange juice: Apple juice = 256 : 160
- The greatest common divisor (GCD) of 256 and 160 is 16.
- Simplifying the ratio gives us 16 : 10, which can be further simplified to 8 : 5.
Cranberry juice to apple juice:
- Cranberry juice: Apple juice = 192 : 160
- The GCD of 192 and 160 is 32.
- Simplifying the ratio gives us 6 : 5.
Apple juice to lemon juice:
- Apple juice: Lemon juice = 160 : 16
- The GCD of 160 and 16 is 16.
- Simplifying the ratio gives us 10 : 1.
Cranberry juice to orange juice:
- Cranberry juice: Orange juice = 192 : 256
- The GCD of 192 and 256 is 64.
- Simplifying the ratio gives us 3 : 4.
Lemon juice to orange juice:
- Lemon juice: Orange juice = 16 : 256
- The GCD of 16 and 256 is 16.
- Simplifying the ratio gives us 1 : 16.
So, the ratios in simplest form are:
- Orange juice to apple juice: 8 : 5
- Cranberry juice to apple juice: 6 : 5
- Apple juice to lemon juice: 10 : 1
- Cranberry juice to orange juice: 3 : 4
- Lemon juice to orange juice: 1 : 16
I hope that helps you with the word problem! Let me know if you have any other questions.
LOL -- a pint is a pound the world around
1 gallon = 4 quarts = 8 pints = 128 oz
so maybe do it all in gallons just for fun :)
orange juice = 2 gal
cranberry = 6 quarts * 1 gal/4 qt = 1.5 gal
apple = 10 pts * 1 gal/8 pt = 1.25 gal
lemon = 16 oz * 1 gal.128 oz = 0.125 gal
now for example:
orange / apple = 2 gal / 1.25 gal = 1.6
Now your turn for the rest