Math / Algebra

QuestionTo babysit one child, Fernando charges $\$ 10$ to drive to the appointment plus $\$ 4$ per hour. He saves $30 \%$ of the total amount he earns. Brenna charges $\$ 6$ per hour and saves $25 \%$ of the total amount she earns. Which equation can be used to determine the number of hours, $h$ , after which Fernando and Brenna will have saved the same amount of money? $10+0.3(4 h)=0.25(6 h)$ $0.3(10)+4 h=0.25(6 h)$ $0.3(10+4 h)=0.25(6 h)$ $0.3(14 h)=0.25(6 h)$

Studdy Solution

STEP 1

What is this asking? How many hours do Fernando and Brenna need to babysit to save the same amount of money? Watch out! Don't forget that Fernando has an initial fee and that both babysitters save portions of their earnings.

STEP 2

1. Define Fernando's earnings
2. Define Brenna's earnings
3. Define Fernando's savings
4. Define Brenna's savings
5. Equate savings and solve for $h$

STEP 3

Fernando earns $\$10$ just for showing up, awesome!
He also earns $\$4$ for every hour he babysits.
If we let $h$ be the number of hours he works, his earnings from the hourly rate are $4 \cdot h$ .

STEP 4

So, Fernando's total earnings are his initial fee plus his hourly earnings: $\$10 + 4 \cdot h$ .

STEP 5

Brenna keeps it simple!
She earns $\$6$ per hour.
So, if she works for $h$ hours, she earns $6 \cdot h$ dollars.

STEP 6

Fernando saves $30\%$ of his total earnings.
Remember, "percent" means "per hundred," so $30\%$ is the same as $\frac{30}{100}$ , which is $0.30$ or just $0.3$ .

STEP 7

To find Fernando's savings, we multiply his total earnings by his savings rate: $0.3 \cdot (10 + 4 \cdot h)$ .

STEP 8

Brenna saves $25\%$ of her earnings.
Similar to Fernando, we convert this percentage to a decimal: $25\% = \frac{25}{100} = 0.25$ .

STEP 9

Brenna's savings are her earnings multiplied by her savings rate: $0.25 \cdot (6 \cdot h)$ .

STEP 10

We want to find when Fernando and Brenna have saved the same amount.
This means their savings are equal!
So we set their savings expressions equal to each other: $0.3 \cdot (10 + 4 \cdot h) = 0.25 \cdot (6 \cdot h)$ .

STEP 11

The equation that can be used to determine the number of hours, $h$ , after which Fernando and Brenna will have saved the same amount of money is $0.3(10+4h)=0.25(6h)$ .
This matches the third option.

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Studdy Solution

STEP 1

What is this asking? How many hours do Fernando and Brenna need to babysit to save the same amount of money? Watch out! Don't forget that Fernando has an initial fee and that both babysitters save portions of their earnings.

STEP 2

1. Define Fernando's earnings
2. Define Brenna's earnings
3. Define Fernando's savings
4. Define Brenna's savings
5. Equate savings and solve for $h$

STEP 3

Fernando earns $\$10$ just for showing up, awesome!
He also earns $\$4$ for every hour he babysits.
If we let $h$ be the number of hours he works, his earnings from the hourly rate are $4 \cdot h$ .

STEP 4

So, Fernando's total earnings are his initial fee plus his hourly earnings: $\$10 + 4 \cdot h$ .

STEP 5

Brenna keeps it simple!
She earns $\$6$ per hour.
So, if she works for $h$ hours, she earns $6 \cdot h$ dollars.

STEP 6

Fernando saves $30\%$ of his total earnings.
Remember, "percent" means "per hundred," so $30\%$ is the same as $\frac{30}{100}$ , which is $0.30$ or just $0.3$ .

STEP 7

To find Fernando's savings, we multiply his total earnings by his savings rate: $0.3 \cdot (10 + 4 \cdot h)$ .

STEP 8

Brenna saves $25\%$ of her earnings.
Similar to Fernando, we convert this percentage to a decimal: $25\% = \frac{25}{100} = 0.25$ .

STEP 9

Brenna's savings are her earnings multiplied by her savings rate: $0.25 \cdot (6 \cdot h)$ .

STEP 10

We want to find when Fernando and Brenna have saved the same amount.
This means their savings are equal!
So we set their savings expressions equal to each other: $0.3 \cdot (10 + 4 \cdot h) = 0.25 \cdot (6 \cdot h)$ .

STEP 11

The equation that can be used to determine the number of hours, $h$ , after which Fernando and Brenna will have saved the same amount of money is $0.3(10+4h)=0.25(6h)$ .
This matches the third option.

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Studdy Solution

STEP 1

What is this asking? How many hours do Fernando and Brenna need to babysit to save the same amount of money? Watch out! Don't forget that Fernando has an initial fee and that both babysitters save *portions* of their earnings.

STEP 2

1. Define Fernando's earnings2. Define Brenna's earnings3. Define Fernando's savings4. Define Brenna's savings5. Equate savings and solve for hhh

STEP 3

Fernando earns $10\$10$10 just for showing up, awesome!He also earns $4\$4$4 for every hour he babysits.If we let hhh be the number of hours he works, his earnings from the hourly rate are 4⋅h4 \cdot h4⋅h.

STEP 4

So, Fernando's *total* earnings are his initial fee plus his hourly earnings: $10+4⋅h\$10 + 4 \cdot h$10+4⋅h.

STEP 5

Brenna keeps it simple!She earns $6\$6$6 per hour.So, if she works for hhh hours, she earns 6⋅h6 \cdot h6⋅h dollars.

STEP 6

Fernando saves 30%30\%30% of his total earnings.Remember, "percent" means "per hundred," so 30%30\%30% is the same as 30100\frac{30}{100}10030​, which is 0.300.300.30 or just 0.30.30.3.

STEP 7

To find Fernando's savings, we multiply his total earnings by his savings rate: 0.3⋅(10+4⋅h)0.3 \cdot (10 + 4 \cdot h)0.3⋅(10+4⋅h).

STEP 8

Brenna saves 25%25\%25% of her earnings.Similar to Fernando, we convert this percentage to a decimal: 25%=25100=0.2525\% = \frac{25}{100} = 0.2525%=10025​=0.25.

STEP 9

Brenna's savings are her earnings multiplied by her savings rate: 0.25⋅(6⋅h)0.25 \cdot (6 \cdot h)0.25⋅(6⋅h).

STEP 10

We want to find when Fernando and Brenna have saved the *same* amount.This means their savings are equal!So we set their savings expressions equal to each other: 0.3⋅(10+4⋅h)=0.25⋅(6⋅h)0.3 \cdot (10 + 4 \cdot h) = 0.25 \cdot (6 \cdot h)0.3⋅(10+4⋅h)=0.25⋅(6⋅h).

STEP 11

The equation that can be used to determine the number of hours, hhh, after which Fernando and Brenna will have saved the same amount of money is 0.3(10+4h)=0.25(6h)0.3(10+4h)=0.25(6h)0.3(10+4h)=0.25(6h).This matches the third option.

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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.

What is this asking? How many hours do Fernando and Brenna need to babysit to save the same amount of money? Watch out! Don't forget that Fernando has an initial fee and that both babysitters save portions of their earnings.

1. Define Fernando's earnings
2. Define Brenna's earnings
3. Define Fernando's savings
4. Define Brenna's savings
5. Equate savings and solve for $h$

Fernando earns $\$10$ just for showing up, awesome!
He also earns $\$4$ for every hour he babysits.
If we let $h$ be the number of hours he works, his earnings from the hourly rate are $4 \cdot h$ .

So, Fernando's total earnings are his initial fee plus his hourly earnings: $\$10 + 4 \cdot h$ .

Brenna keeps it simple!
She earns $\$6$ per hour.
So, if she works for $h$ hours, she earns $6 \cdot h$ dollars.

Fernando saves $30\%$ of his total earnings.
Remember, "percent" means "per hundred," so $30\%$ is the same as $\frac{30}{100}$ , which is $0.30$ or just $0.3$ .

To find Fernando's savings, we multiply his total earnings by his savings rate: $0.3 \cdot (10 + 4 \cdot h)$ .

Brenna saves $25\%$ of her earnings.
Similar to Fernando, we convert this percentage to a decimal: $25\% = \frac{25}{100} = 0.25$ .

Brenna's savings are her earnings multiplied by her savings rate: $0.25 \cdot (6 \cdot h)$ .

We want to find when Fernando and Brenna have saved the same amount.
This means their savings are equal!
So we set their savings expressions equal to each other: $0.3 \cdot (10 + 4 \cdot h) = 0.25 \cdot (6 \cdot h)$ .

The equation that can be used to determine the number of hours, $h$ , after which Fernando and Brenna will have saved the same amount of money is $0.3(10+4h)=0.25(6h)$ .
This matches the third option.