Suppose you have $55 in your account. You start saving $10 each week. Your friend has $20 in her account and is saving $15 each week.
A) When will you and your friend have the same amount of money in your accounts?
B) How much money will each of you have?
A) To find out when you and your friend will have the same amount of money, we can set up an equation. Let's call the number of weeks it takes for you both to have the same amount of money "x".
For you: 55 + 10x
For your friend: 20 + 15x
To find the point where you both have the same amount of money, we need to set these two amounts equal to each other:
55 + 10x = 20 + 15x
Now, let's solve this equation for "x":
55 - 20 = 15x - 10x
35 = 5x
x = 7
Therefore, it will take 7 weeks for you and your friend to have the same amount of money in your accounts.
B) To find out how much money each of you will have after 7 weeks, we can substitute the value of "x" into the equations we previously set up.
For you: 55 + 10(7) = 55 + 70 = $125
For your friend: 20 + 15(7) = 20 + 105 = $125
Therefore, after 7 weeks, both you and your friend will have $125 in your accounts.
To find the answers to these questions, we can set up equations and solve for the unknown variables. Let's label the number of weeks as "w" and the amount of money in your account as "M" and your friend's account as "F."
A) When will you and your friend have the same amount of money in your accounts?
To find the time when you both have the same amount of money, we need to set up an equation:
Your account balance: M = $55 + $10w
Friend's account balance: F = $20 + $15w
To find when the balances are equal, we set M equal to F and solve for "w":
$55 + $10w = $20 + $15w
Subtract $10w from both sides:
$55 = $20 + $5w
Subtract $20 from both sides:
$35 = $5w
Divide both sides by $5:
7 = w
Therefore, you and your friend will have the same amount of money after 7 weeks.
B) How much money will each of you have?
To determine the amount of money you and your friend will have after 7 weeks, substitute the value of "w" into the respective equations:
Your account balance (M): M = $55 + $10w
Substituting w = 7:
M = $55 + $10(7)
M = $55 + $70
M = $125
Your account balance will be $125 after 7 weeks.
Friend's account balance (F): F = $20 + $15w
Substituting w = 7:
F = $20 + $15(7)
F = $20 + $105
F = $125
Your friend's account balance will also be $125 after 7 weeks.
So, after 7 weeks, both you and your friend will have $125 in your accounts.
let number of weeks be w
solve
10w + 55 = 15w + 20
take it from there
10w+55=15w+20
-10w -10w
55=5w+20
-20 -20
35=5w
/5 /5
7=w