Math / Algebra

QuestionJames has some apples and oranges. The ratio of apples and oranges is $2: 5$ He has 15 oranges. How many apples does James have?

Studdy Solution

STEP 1

What is this asking? If James has a bunch of apples and oranges, and we know the relative amounts of each fruit and the exact number of oranges, how many apples does he have? Watch out! Don't mix up the ratio.
It's apples TO oranges, not the other way around!

STEP 2

1. Set up the ratio.
2. Solve for the number of apples.

STEP 3

Alright, so we know the ratio of apples to oranges is $2:5$ .
This means for every 2 apples, James has 5 oranges.
Let's write this as a fraction, where the number of apples is in the numerator and the number of oranges is in the denominator: $\frac{\text{Number of Apples}}{\text{Number of Oranges}} = \frac{2}{5}$ .

STEP 4

We know James has 15 oranges.
Let's plug that into our fraction, replacing "Number of Oranges" with 15: $\frac{\text{Number of Apples}}{15} = \frac{2}{5}$ .

STEP 5

To find the number of apples, we need to isolate "Number of Apples" on one side of the equation.
Right now, it's being divided by 15.
To undo this division, we can multiply both sides of the equation by 15.
Remember, what we do to one side, we must do to the other to keep things balanced!

STEP 6

So, we have $15 \cdot \frac{\text{Number of Apples}}{15} = \frac{2}{5} \cdot 15$ .
On the left side, the 15s divide to one, leaving us with just the Number of Apples.
Awesome!

STEP 7

On the right side, we have $\frac{2}{5} \cdot 15$ .
We can think of 15 as $\frac{15}{1}$ .
So, $\frac{2}{5} \cdot \frac{15}{1} = \frac{2 \cdot 15}{5 \cdot 1} = \frac{30}{5}$ .
Now, we divide 30 by 5, which gives us 6.

STEP 8

Therefore, $\text{Number of Apples} = 6$ .

STEP 9

James has 6 apples.

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QuestionJames has some apples and oranges. The ratio of apples and oranges is $2: 5$ He has 15 oranges. How many apples does James have?

Studdy Solution

STEP 1

What is this asking? If James has a bunch of apples and oranges, and we know the relative amounts of each fruit and the exact number of oranges, how many apples does he have? Watch out! Don't mix up the ratio.
It's apples TO oranges, not the other way around!

STEP 2

1. Set up the ratio.
2. Solve for the number of apples.

STEP 3

STEP 4

We know James has 15 oranges.
Let's plug that into our fraction, replacing "Number of Oranges" with 15: $\frac{\text{Number of Apples}}{15} = \frac{2}{5}$ .

STEP 5

To find the number of apples, we need to isolate "Number of Apples" on one side of the equation.
Right now, it's being divided by 15.
To undo this division, we can multiply both sides of the equation by 15.
Remember, what we do to one side, we must do to the other to keep things balanced!

STEP 6

So, we have $15 \cdot \frac{\text{Number of Apples}}{15} = \frac{2}{5} \cdot 15$ .
On the left side, the 15s divide to one, leaving us with just the Number of Apples.
Awesome!

STEP 7

On the right side, we have $\frac{2}{5} \cdot 15$ .
We can think of 15 as $\frac{15}{1}$ .
So, $\frac{2}{5} \cdot \frac{15}{1} = \frac{2 \cdot 15}{5 \cdot 1} = \frac{30}{5}$ .
Now, we divide 30 by 5, which gives us 6.

STEP 8

Therefore, $\text{Number of Apples} = 6$ .

STEP 9

James has 6 apples.

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QuestionJames has some apples and oranges. The ratio of apples and oranges is 2:52: 52:5 He has 15 oranges. How many apples does James have?

Studdy Solution

STEP 1

What is this asking? If James has a bunch of apples and oranges, and we know the relative amounts of each fruit and the exact number of oranges, how many apples does he have? Watch out! Don't mix up the ratio.It's apples TO oranges, not the other way around!

STEP 2

1. Set up the ratio.2. Solve for the number of apples.

STEP 3

STEP 4

We know James has **15 oranges**.Let's plug that into our fraction, replacing "Number of Oranges" with **15**: Number of Apples15=25\frac{\text{Number of Apples}}{15} = \frac{2}{5}15Number of Apples​=52​.

STEP 5

STEP 6

So, we have 15⋅Number of Apples15=25⋅1515 \cdot \frac{\text{Number of Apples}}{15} = \frac{2}{5} \cdot 1515⋅15Number of Apples​=52​⋅15.On the left side, the **15s divide to one**, leaving us with just the **Number of Apples**.Awesome!

STEP 7

STEP 8

Therefore, Number of Apples=6\text{Number of Apples} = 6Number of Apples=6.

STEP 9

James has **6 apples**.

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Studdy solves anything!

Start learning now

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

QuestionJames has some apples and oranges. The ratio of apples and oranges is $2: 5$ He has 15 oranges. How many apples does James have?

What is this asking? If James has a bunch of apples and oranges, and we know the relative amounts of each fruit and the exact number of oranges, how many apples does he have? Watch out! Don't mix up the ratio.
It's apples TO oranges, not the other way around!

1. Set up the ratio.
2. Solve for the number of apples.

We know James has 15 oranges.
Let's plug that into our fraction, replacing "Number of Oranges" with 15: $\frac{\text{Number of Apples}}{15} = \frac{2}{5}$ .

So, we have $15 \cdot \frac{\text{Number of Apples}}{15} = \frac{2}{5} \cdot 15$ .
On the left side, the 15s divide to one, leaving us with just the Number of Apples.
Awesome!

Therefore, $\text{Number of Apples} = 6$ .

James has 6 apples.