Answer :
Below is a step-by-step solution for each part.
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Part (a):
Andre drinks 15 ounces of water, which is [tex]\(\frac{3}{4}\)[/tex] of the bottle. Let [tex]\( x \)[/tex] represent the total number of ounces the bottle can hold. The situation can be expressed by the equation
[tex]$$
\frac{3}{4}x = 15.
$$[/tex]
To solve for [tex]\( x \)[/tex], multiply both sides of the equation by the reciprocal of [tex]\(\frac{3}{4}\)[/tex] (which is [tex]\(\frac{4}{3}\)[/tex]):
[tex]$$
x = 15 \times \frac{4}{3} = 20.
$$[/tex]
Thus, the bottle holds [tex]\(20\)[/tex] ounces of water.
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Part (b):
A bottle holds [tex]\(15\)[/tex] ounces of water and Jada drinks [tex]\(8.5\)[/tex] ounces of water. Let [tex]\( y \)[/tex] represent the number of ounces remaining in the bottle. The quantity left can be found by subtracting the amount Jada drank from the total water:
[tex]$$
y = 15 - 8.5.
$$[/tex]
Calculating the above gives
[tex]$$
y = 6.5.
$$[/tex]
So, there are [tex]\(6.5\)[/tex] ounces of water left in the bottle.
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Part (c):
A bottle holds [tex]\( z \)[/tex] ounces of water, and a second bottle holds [tex]\(16\)[/tex] ounces, which is twice as much as the first bottle. This can be modeled with the equation
[tex]$$
16 = 2z.
$$[/tex]
Solve for [tex]\( z \)[/tex] by dividing both sides by [tex]\(2\)[/tex]:
[tex]$$
z = \frac{16}{2} = 8.
$$[/tex]
Therefore, the first bottle holds [tex]\(8\)[/tex] ounces of water.
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Summary of Answers:
- (a) The bottle holds [tex]\(20\)[/tex] ounces of water.
- (b) There are [tex]\(6.5\)[/tex] ounces of water left.
- (c) The first bottle holds [tex]\(8\)[/tex] ounces of water.
──────────────────────────────
Part (a):
Andre drinks 15 ounces of water, which is [tex]\(\frac{3}{4}\)[/tex] of the bottle. Let [tex]\( x \)[/tex] represent the total number of ounces the bottle can hold. The situation can be expressed by the equation
[tex]$$
\frac{3}{4}x = 15.
$$[/tex]
To solve for [tex]\( x \)[/tex], multiply both sides of the equation by the reciprocal of [tex]\(\frac{3}{4}\)[/tex] (which is [tex]\(\frac{4}{3}\)[/tex]):
[tex]$$
x = 15 \times \frac{4}{3} = 20.
$$[/tex]
Thus, the bottle holds [tex]\(20\)[/tex] ounces of water.
──────────────────────────────
Part (b):
A bottle holds [tex]\(15\)[/tex] ounces of water and Jada drinks [tex]\(8.5\)[/tex] ounces of water. Let [tex]\( y \)[/tex] represent the number of ounces remaining in the bottle. The quantity left can be found by subtracting the amount Jada drank from the total water:
[tex]$$
y = 15 - 8.5.
$$[/tex]
Calculating the above gives
[tex]$$
y = 6.5.
$$[/tex]
So, there are [tex]\(6.5\)[/tex] ounces of water left in the bottle.
──────────────────────────────
Part (c):
A bottle holds [tex]\( z \)[/tex] ounces of water, and a second bottle holds [tex]\(16\)[/tex] ounces, which is twice as much as the first bottle. This can be modeled with the equation
[tex]$$
16 = 2z.
$$[/tex]
Solve for [tex]\( z \)[/tex] by dividing both sides by [tex]\(2\)[/tex]:
[tex]$$
z = \frac{16}{2} = 8.
$$[/tex]
Therefore, the first bottle holds [tex]\(8\)[/tex] ounces of water.
──────────────────────────────
Summary of Answers:
- (a) The bottle holds [tex]\(20\)[/tex] ounces of water.
- (b) There are [tex]\(6.5\)[/tex] ounces of water left.
- (c) The first bottle holds [tex]\(8\)[/tex] ounces of water.
