Math / Algebra

QuestionJim currently has \ $1,250 in his bank account and Sally has$ \ $1,400$ in her bank account. Jim deposits $\$ 27.50$ per week and Sally deposits $\$ 20$ per week into her account. After how many weeks will they have the same amount of money?

Studdy Solution

STEP 1

1. Jim starts with $1,250 in his bank account.<br />2. Sally starts with$ 1,400 in her bank account.
3. Jim deposits $27.50 per week.<br />4. Sally deposits$ 20 per week.
5. We need to find the number of weeks after which they will have the same amount of money.

STEP 2

1. Define variables for the number of weeks.
2. Write expressions for the total amount of money in each account after a certain number of weeks.
3. Set the expressions equal to each other to find when the amounts are the same.
4. Solve the equation for the number of weeks.

STEP 3

Define a variable for the number of weeks. Let $w$ represent the number of weeks after which Jim and Sally will have the same amount of money.

STEP 4

Write expressions for the total amount of money in each account after $w$ weeks.
For Jim, the total amount after $w$ weeks is: $1250 + 27.50w$
For Sally, the total amount after $w$ weeks is: $1400 + 20w$

STEP 5

Set the expressions equal to each other to find when the amounts are the same.
$1250 + 27.50w = 1400 + 20w$

STEP 6

Solve the equation for $w$ .
First, subtract $20w$ from both sides: $1250 + 7.50w = 1400$
Next, subtract 1250 from both sides: $7.50w = 150$
Finally, divide both sides by 7.50: $w = \frac{150}{7.50}$ $w = 20$
Jim and Sally will have the same amount of money after $\boxed{20}$ weeks.

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QuestionJim currently has \ $1,250 in his bank account and Sally has$ \ $1,400$ in her bank account. Jim deposits $\$ 27.50$ per week and Sally deposits $\$ 20$ per week into her account. After how many weeks will they have the same amount of money?

Studdy Solution

STEP 1

1. Jim starts with $1,250 in his bank account.<br />2. Sally starts with$ 1,400 in her bank account.
3. Jim deposits $27.50 per week.<br />4. Sally deposits$ 20 per week.
5. We need to find the number of weeks after which they will have the same amount of money.

STEP 2

1. Define variables for the number of weeks.
2. Write expressions for the total amount of money in each account after a certain number of weeks.
3. Set the expressions equal to each other to find when the amounts are the same.
4. Solve the equation for the number of weeks.

STEP 3

Define a variable for the number of weeks. Let $w$ represent the number of weeks after which Jim and Sally will have the same amount of money.

STEP 4

Write expressions for the total amount of money in each account after $w$ weeks.
For Jim, the total amount after $w$ weeks is: $1250 + 27.50w$
For Sally, the total amount after $w$ weeks is: $1400 + 20w$

STEP 5

Set the expressions equal to each other to find when the amounts are the same.
$1250 + 27.50w = 1400 + 20w$

STEP 6

Solve the equation for $w$ .
First, subtract $20w$ from both sides: $1250 + 7.50w = 1400$
Next, subtract 1250 from both sides: $7.50w = 150$
Finally, divide both sides by 7.50: $w = \frac{150}{7.50}$ $w = 20$
Jim and Sally will have the same amount of money after $\boxed{20}$ weeks.

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Studdy Solution

STEP 1

STEP 2

1. Define variables for the number of weeks.2. Write expressions for the total amount of money in each account after a certain number of weeks.3. Set the expressions equal to each other to find when the amounts are the same.4. Solve the equation for the number of weeks.

STEP 3

Define a variable for the number of weeks. Let w w w represent the number of weeks after which Jim and Sally will have the same amount of money.

STEP 4

Write expressions for the total amount of money in each account after w w w weeks.For Jim, the total amount after w w w weeks is: 1250+27.50w 1250 + 27.50w 1250+27.50wFor Sally, the total amount after w w w weeks is: 1400+20w 1400 + 20w 1400+20w

STEP 5

Set the expressions equal to each other to find when the amounts are the same.1250+27.50w=1400+20w 1250 + 27.50w = 1400 + 20w 1250+27.50w=1400+20w

STEP 6

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Start learning now

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

1. Define variables for the number of weeks.
2. Write expressions for the total amount of money in each account after a certain number of weeks.
3. Set the expressions equal to each other to find when the amounts are the same.
4. Solve the equation for the number of weeks.

Define a variable for the number of weeks. Let $w$ represent the number of weeks after which Jim and Sally will have the same amount of money.

Write expressions for the total amount of money in each account after $w$ weeks.
For Jim, the total amount after $w$ weeks is: $1250 + 27.50w$
For Sally, the total amount after $w$ weeks is: $1400 + 20w$

Set the expressions equal to each other to find when the amounts are the same.
$1250 + 27.50w = 1400 + 20w$