Solved on Jan 22, 2024

Find the amount of pineapple juice needed for a punch with a $4:3$ ratio of orange to pineapple juice, given $64$ oz of orange juice.

STEP 1

Assumptions
1. The ratio of orange juice to pineapple juice is 4:3.
2. Bill has 64 oz of orange juice.

STEP 2

To find out how much pineapple juice Bill needs, we will use the given ratio. The ratio tells us that for every 4 parts of orange juice, we need 3 parts of pineapple juice.

STEP 3

Let's denote the amount of pineapple juice needed as $x$ oz. According to the ratio, we can set up the following proportion:
$\frac{orange\,juice}{pineapple\,juice} = \frac{4}{3}$

STEP 4

Now we can express the proportion in terms of the known quantity of orange juice (64 oz) and the unknown quantity of pineapple juice ( $x$ oz):
$\frac{64}{x} = \frac{4}{3}$

STEP 5

To solve for $x$ , we cross-multiply:
$3 \times 64 = 4 \times x$

STEP 6

Perform the multiplication on the left side of the equation:
$192 = 4 \times x$

STEP 7

Now, divide both sides of the equation by 4 to solve for $x$ :
$\frac{192}{4} = x$

STEP 8

Calculate the value of $x$ :
$x = \frac{192}{4} = 48$

STEP 9

So, Bill needs 48 oz of pineapple juice to maintain the ratio of 4:3 with the 64 oz of orange juice he has.
Bill needs to add 48 oz of pineapple juice.

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Find the amount of pineapple juice needed for a punch with a $4:3$ ratio of orange to pineapple juice, given $64$ oz of orange juice.

STEP 1

Assumptions
1. The ratio of orange juice to pineapple juice is 4:3.
2. Bill has 64 oz of orange juice.

STEP 2

To find out how much pineapple juice Bill needs, we will use the given ratio. The ratio tells us that for every 4 parts of orange juice, we need 3 parts of pineapple juice.

STEP 3

Let's denote the amount of pineapple juice needed as $x$ oz. According to the ratio, we can set up the following proportion:
$\frac{orange\,juice}{pineapple\,juice} = \frac{4}{3}$

STEP 4

Now we can express the proportion in terms of the known quantity of orange juice (64 oz) and the unknown quantity of pineapple juice ( $x$ oz):
$\frac{64}{x} = \frac{4}{3}$

STEP 5

To solve for $x$ , we cross-multiply:
$3 \times 64 = 4 \times x$

STEP 6

Perform the multiplication on the left side of the equation:
$192 = 4 \times x$

STEP 7

Now, divide both sides of the equation by 4 to solve for $x$ :
$\frac{192}{4} = x$

STEP 8

Calculate the value of $x$ :
$x = \frac{192}{4} = 48$

STEP 9

So, Bill needs 48 oz of pineapple juice to maintain the ratio of 4:3 with the 64 oz of orange juice he has.
Bill needs to add 48 oz of pineapple juice.

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Find the amount of pineapple juice needed for a punch with a 4:34:34:3 ratio of orange to pineapple juice, given 646464 oz of orange juice.

STEP 1

Assumptions1. The ratio of orange juice to pineapple juice is 4:3.2. Bill has 64 oz of orange juice.

STEP 2

To find out how much pineapple juice Bill needs, we will use the given ratio. The ratio tells us that for every 4 parts of orange juice, we need 3 parts of pineapple juice.

STEP 3

Let's denote the amount of pineapple juice needed as x x x oz. According to the ratio, we can set up the following proportion:orange juicepineapple juice=43 \frac{orange\,juice}{pineapple\,juice} = \frac{4}{3} pineapplejuiceorangejuice​=34​

STEP 4

Now we can express the proportion in terms of the known quantity of orange juice (64 oz) and the unknown quantity of pineapple juice (x x x oz):64x=43 \frac{64}{x} = \frac{4}{3} x64​=34​

STEP 5

To solve for x x x, we cross-multiply:3×64=4×x 3 \times 64 = 4 \times x 3×64=4×x

STEP 6

Perform the multiplication on the left side of the equation:192=4×x 192 = 4 \times x 192=4×x

STEP 7

Now, divide both sides of the equation by 4 to solve for x x x:1924=x \frac{192}{4} = x 4192​=x

STEP 8

Calculate the value of x x x:x=1924=48 x = \frac{192}{4} = 48 x=4192​=48

STEP 9

So, Bill needs 48 oz of pineapple juice to maintain the ratio of 4:3 with the 64 oz of orange juice he has.Bill needs to add 48 oz of pineapple juice.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the amount of pineapple juice needed for a punch with a $4:3$ ratio of orange to pineapple juice, given $64$ oz of orange juice.

Assumptions
1. The ratio of orange juice to pineapple juice is 4:3.
2. Bill has 64 oz of orange juice.

Let's denote the amount of pineapple juice needed as $x$ oz. According to the ratio, we can set up the following proportion:
$\frac{orange\,juice}{pineapple\,juice} = \frac{4}{3}$

Now we can express the proportion in terms of the known quantity of orange juice (64 oz) and the unknown quantity of pineapple juice ( $x$ oz):
$\frac{64}{x} = \frac{4}{3}$

To solve for $x$ , we cross-multiply:
$3 \times 64 = 4 \times x$

Perform the multiplication on the left side of the equation:
$192 = 4 \times x$

Now, divide both sides of the equation by 4 to solve for $x$ :
$\frac{192}{4} = x$

Calculate the value of $x$ :
$x = \frac{192}{4} = 48$

So, Bill needs 48 oz of pineapple juice to maintain the ratio of 4:3 with the 64 oz of orange juice he has.
Bill needs to add 48 oz of pineapple juice.