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

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.

Answer 2

Andre saves more money than Elena after four weeks and after 6 weeks the savings of Andre and Elena is the same and this can be determined by forming the linear equation.

Given :

• 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.

Let w represents the total number of weeks. So, the linear equation that represents the situatuion "Andre starts with $100 in his savings account and adds $5 per week" is:

S = 5w + 100

The linear equation that represents the situatuion "Elena starts with $10 in her savings account and adds $20 each week" is:

S' = 20w + 10

a) After four weeks the savings of Andre is given by:

S = 5(4) + 100

S = 20 + 100

S = $120

After four weeks the savings of Elena is given by:

S' = 20(4) + 10

S' = 80 + 10

S' = $90

So, Andre saves more money than Elena after four weeks.

b) Now, the number of weeks after which the savings of Andre and Elena are the same is:

5w + 100 = 20w + 10

Simplify the above equation in order to determine the value of 'w'.

90 = 15w

w = 6

So, after 6 weeks the savings of Andre and Elena is the same.

For more information, refer to the link given below:

https://brainly.com/question/21835898