1.) You have $22 in your bank account, and you deposit $11.50 per week. Your cousin has $218 in his bank account and is withdrawing $13 per week. The graph of this problem situation intersects at x=8. What does this mean?






A.
In 8 weeks, you will have triple the amount of money in your account.




B.
In 8 weeks, your cousin will run out of money.




C.
In 8 weeks, both bank accounts will have the same amount of money in them.




D.
In 8 weeks, you will break-even.



2.) A garden supply store sells two types of lawn mowers. The cashiers kept a tally chart for the total number of mowers sold. They tallied 30 mowers sold. Total sales of mowers for the year were $8379.70. The small mowers cost $249.99 and the large mowers cost $329.99. Find the number of each type of mower sold.





A.
The store did not sell any small mowers. They sold 25 large mowers.




B.
The store sold 8 small mowers and 22 large mowers.




C.
The store sold 11 small mowers and 19 large mowers.




D.
The store sold 8 more small mowers than large mowers.



3.) Molly is selling bracelets and necklaces for her friend at a craft fair. The cost of 4 bracelets and 3 necklaces is $23.50. The cost of 5 bracelets and 2 necklaces
is $21.50 The system of equations that follows represents the situation.{4b+3n=23.50 {5b+2n=21.50 A customer wanted to buy just one bracelet and just one necklace.
How much money should Molly charge the customer?

first one:

your equation:
B = 22 +11.5w , where B is the balance, and w is the number of weeks
or
y = 22+11.5x to make it fit your x = 8

your friend:
y = 218-13x
if x = 8,
you will have 22+11.5(8) = 114
your friend has 218-13(8) = 114

What do you think?

Give the other two a shot using a similar method

I got #1 C, #2 D and #3 $6.50?

#2 is correct

#3 solving your 2 equations:
1st times 2: 8b+6n=47
2nd times 3: 15b+6n=64.5
subtract them:
7b = 17.5
b = 2.5
sub back in ----> n = 4.5

necklace costs $4.50 and bracelet costs $2.50
so buying just one each = $7.00

Was #1 correct?

1.) To solve this problem, we need to analyze the situation described in the problem and the graph that represents it. The x-coordinate of the point where the graph intersects is given as 8. This corresponds to 8 weeks.

To determine the meaning of this intersection, we need to compare the amounts of money in the two bank accounts at this point.

In 8 weeks, the amount of money in your account would be $22 + ($11.50/week * 8 weeks) = $22 + $92 = $114.

In 8 weeks, the amount of money in your cousin's account would be $218 - ($13/week * 8 weeks) = $218 - $104 = $114.

Both bank accounts will have the same amount of money in them, which means the answer is C. In 8 weeks, both bank accounts will have the same amount of money in them.

2.) To find the number of each type of mower sold, we can set up a system of equations using the given information.

Let's assume x is the number of small mowers sold and y is the number of large mowers sold.

From the information given, we can set up the following equations:

x + y = 30 (equation 1) - This equation represents the total number of mowers sold.

249.99x + 329.99y = 8379.70 (equation 2) - This equation represents the total sales of mowers for the year.

To solve this system of equations, we can use substitution or elimination method.

Using the elimination method, we can multiply equation 1 by 249.99 and subtract it from equation 2 to eliminate x:

(249.99x + 249.99y) - (249.99x + 329.99y) = 8379.70 - (249.99 * 30)

-80y = 8379.70 - 7499.7

-80y = 880

y = -880 / -80

y = 11

Substituting the value of y back into equation 1, we can solve for x:

x + 11 = 30

x = 30 - 11

x = 19

Therefore, the store sold 19 small mowers and 11 large mowers, which means the answer is C. The store sold 11 small mowers and 19 large mowers.

3.) To determine how much money Molly should charge the customer, we need to solve the system of equations given.

The system of equations is:

4b + 3n = 23.50 (equation 1)

5b + 2n = 21.50 (equation 2)

To solve this system of equations, we can use substitution or elimination method.

Let's use the elimination method. Multiply equation 1 by 5 and equation 2 by 4 to eliminate b:

20b + 15n = 117.5 (equation 3)

20b + 8n = 86 (equation 4)

Subtract equation 4 from equation 3:

(20b + 15n) - (20b + 8n) = 117.5 - 86

7n = 31.5

n = 31.5 / 7

n = 4.5

Substituting the value of n back into equation 1, we can solve for b:

4b + 3(4.5) = 23.50

4b + 13.5 = 23.50

4b = 23.50 - 13.5

4b = 10

b = 10 / 4

b = 2.5

Therefore, Molly should charge the customer $2.50 for the bracelet and $4.50 for the necklace, which means the answer is $7.