Question

6. Andre and Elena are each saving money. Andre starts with $100 in his savings account and adds $5 per week. Elena starts with $10 in her savings account and adds $20 each week.
a. After four weeks, who has more money in the
who has more money in their savings account? Explain how you know.
b. after how many weeks will Andre and Elena have the same amount of money in their savings
accounts?

Answer 1

Step-by-step explanation:

So, first Andre is starting with 100 dollars in his savings account. Every week, he adds 5 dollars. And Elena starts with 10 dollars and adds 20 dollars per week.

1. Solve what Andre did.

$5 multiplied by 4 weeks = $20. So, $100 + $20 = $120.

2. Solve what Elena did.

$20 × 4 weeks = $80. $10 from her savings account + $80 = $90

3. So, Andre has more money because he started with $100, which is lots of money. And Elena only started with $10. So, Andre has $30 more than Elena.

4. For Part B, you have to count how many weeks in order for both of them to have the same amount of money left in their savings account.

5. Since Andre gets $5 a week, he can get at least 2 weeks and get $130. And for Elena, she would have to do 2 weeks also. For now she has $90, but for two weeks would be $130.

Answer for Part B: Each of them would have to do 2 weeks to get the same amount. (Which is 4 weeks)

Answer 2

You need to write an equation for each.

For Andre, he has 100 dollars, and every week gets 5 dollars more. You add the 5 dollars, and Since you don't know how many weeks it has been, use a variable.

$100 + 5w$

For Elena, she has 10 dollars, and gets 20 each week.

$10 + 20w$

Now that you know that it has been 4 weeks, you can plug in 4 for the variable for weeks.

Andrew:

$100 + 5(4) = 100 + 20 = 120$

Elena

$10 + 20(4) = 10 + 80 = 90$

Andrew has more money in this time.

To find when they have the same amount, equal their expressions to each other. This means that they will have the same amount (because they are equalled) and you can solve to find the variable, which means the weeks that they are equal at.

Bring the like terms to each side by canceling them out. Since you have positive 10, then subtract 10 to each side. You have 5w, so subtract 5w to each side.

$100 + 5w = 10 + 20w \\ 90 + 5w = 20w \\ 90 = 15w \\ 90 \div 15 = 6 \\ 6 = w$

The answer will simplify down to 6 weeks.