8th grade algebra please help!?

Question

QUESTION:1.Susan wants to have business cards printed. One style costs $25 plus 2 cents per card. Another style will cost $10 plus 5 cents per card. For how many cards will the cost be the same for both styles?





QUESTION:2.Lorena bought 10 packs of styrofoam cups for the graduation dance. A pack of fifty 12 oz cups costs $1.80 and a pack of fifty 16-oz cups costs $2.40. Lorena paid a total of $21.60 excluding tax. How many packs of paper cups did she buy?





QUESTION:3.Safety Rent-A-Truck rents a truck at a daily rate of $57.99 plus 48 cents per mile. City Rentals rents the same size truck for $58.95 plus plus 46 cents per mile. For what mileage is the cost the same?




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This is really hard for me and I've been stressed for 2 days with this kind of math. Can you please help?
And could you please show your work. I completely DONT GET IT.

Answer 1

Question 1

25 + 0.02 *n = 10 + 0.05*n
0.05n - 0.02n = 25 - 10
0.03n = 15 => n= 15/0.03 = 500
so the number of cards that makes both styles cost the same is 500


Question2:

let x be the number of 12 oz cups and y the number of 16 oz cups

x + y =10 (since she bought a total of 10 cups)
1.8 x + 2.4 y = 21.6 (total she paid for the cups)

solving the system of equation:
x = 10 - y
1.8x + 2.4y = 21.6

1.8 (10 - y) + 2.4y = 21.6
0.6y = 21.6 - 18 = 3.6
y = 3.6/0.6 = 6
x = 4

she bought 4 packs of 12 oz cups and 6 packs of 16 oz cups


question3:

same as the first problem
57.99 + 0.48m = 58.95 + 0.46m
0.02m = 0.96
m= 48 miles

so the number of milage is 48

Answer 2

QUESTION:1.Susan wants to have business cards printed. One style costs $25 plus 2 cents per card. Another style will cost $10 plus 5 cents per card. For how many cards will the cost be the same for both styles?

25 + 0.02x = 10 + 0.05x

QUESTION:2.Lorena bought 10 packs of Styrofoam cups for the graduation dance. A pack of fifty 12 oz cups costs $1.80 and a pack of fifty 16-oz cups costs $2.40. Lorena paid a total of $21.60 excluding tax. How many packs of paper cups did she buy?

None. She bought Styrofoam cups.
If x = the number of 12 oz cups,
$1.80x + $2.40(10 - x) = $21.60

QUESTION:3.Safety Rent-A-Truck rents a truck at a daily rate of $57.99 plus 48 cents per mile. City Rentals rents the same size truck for $58.95 plus plus 46 cents per mile. For what mileage is the cost the same?

This one is the same as the 1st one, just different numbers:

57.99 + 0.48x = 58.95 + 0.46x

Answer 3

1) If one style costs $25 plus 2 cents per card, then getting X number of cards in that style will cost a total of
25 + 0.02X dollars. If the other style costs $10 plus 5 cents per card, then getting X number of cards in that style will cost a total of 10 + 0.05X dollars. We want to find out what value of X will make both of these totals the same. So if they're supposed to be the same, set them equal to each other:
25 + 0.02X = 10 + 0.05X
Now you have one equation with one variable, and you want to find the value of X. So just use algebra now to solve for X.

2) Well they TELL us that she bought 10 packs, so we could sarcastically answer "10". Or we could could answer zero to the actual question of "How many packs of PAPER cups did she buy" becuase she bought styrofoam! But we'll assume they mean how much of each type did she buy.

Let T be the number of packages she bought of twelve-ounce cups. Let S be the number of sixteen-ounce cup packages she bought. We're told that she bought a total of 10 packs all together, so T+S=10. The twelve-ounce packs cost $1.80 each, so the money she spent on twelve-ounce cups is 1.80T. Likewise, the money she spent on sixteen-ounce cups is 2.40S. Together, we're told this cost $21.60. So 1.80T + 2.40S = 21.60.
You now have two equations with two unknowns, T and S. Use substitution to solve for T and S.

Somebody suggested using only one of these equations and then doing a "guess and check". This is very bad way to go about problems like these, especially since in other similar problems it would take too long to do.

3) Use the same technique you used in #1. Get an expression for the total cost in each case where (say) M is the mileage for both. Set the expressions equal to each other and solve for M.

Answer 4

Ok so whenever we do not know what a value is we put in a variable. For the first question we do not know how many cards we need therefore we will use x.

We know that the two values must equal each other so for now what we have is:
x = x .

We must now put in the other values in our problem. One style costs $25 + 2 cents per card. let's write 2 cents as .02 just to keep things consistent. Since x is the amount of cards it must be .02x plus the amount for the style which is $25. The same goes for the other style except .05x plus $10

We now have the equation:
.02x+25=.05x+10
We want to isolate the x so we subtract 10 from each side and get:
.02x+15=.05x
Next we subtract .02x from each side so x is alone on one side:
15=.03x
We divide both sides by .03:
500=x
Since x is the variable for how many cards, 500 cards would make the cost equivalent.

Answer 5

Question 1:

let x = # of cards bought for either price

25 + 0.02x = 10 + 0.05x

solve for x:

15 = 0.03x
500 = x

Therefore, Susan would have to buy 500 cards of both styles for the cost to be the same.

CHECK (replace x by 500):

25 + 500(0.02) = 10 + 500(0.05)
$35 = $35


Question 2:

let x = # of 12 oz. cup packs
let y = # of 16 oz. cup packs

There are 2 equations that can be set up with the given information:

x + y = 10
1.8x + 2.4y = 21.60

solve for x (or y) in either of the 2 above equations; I will perform it for the first one above:

x = 10 - y

now, substitute (x = 10 - y) into the second equation and solve:

1.8(10 - y) + 2.4y = 21.60
18 - 1.8y + 2.4y = 21.60
0.6y = 3.6
y = 6 (# of 16 oz. cup packs)
x = 4 (# of 12 oz. cup packs)

CHECK (by substituting x and y values in both equations:

x + y = 10 = 6 + 4
4(1.8) + 6(2.4) = 21.60


Question 3 (similar to Question 1 above):

let x = # of miles

57.99 + 0.48x = 58.95 + 0.46x

solve for x:

0.02x = 0.96
x = 48 miles

CHECK (replace x by 48):

57.99 + 48(0.48) = 58.95 + 48(0.46)
81.03 = 81.03

Answer 6

Q1.
Style A. 25+0.02x = the cost depending on how many cards
Style B. 10+0.05x = the cost depending on how many cards
x is the number of cards to be printed.
So You just put together it like this.

25+0.02x = 10+0.05x

And you start moving the numbers from one side of the equal sign to the oher. (Inverting signs, of course)

25 - 10 +0.02x = 0.05x
(25 - 10) +0.02x = 0.05x
(15) +0.02x = 0.05x
15 = 0.05x -0.02x
15 = (0.05 -0.02)x
15 = (0.03)x
15 = 0.03x
(15 / 0.03)= x
500=x
x=500

You should be able to do the same for the other questions. Piece of Cake.

Answer 7

1.) 25+.02x
25 being the initial cost
.02 being per card (x being number of cards)

10+.05x

so when

25+.02x=10+.05x
Subtract 10 from both sides

15+.02x=.05x
Subtract .02x from both sides

15=.03x
Divide by .03 on both sides

500=x

500 cards

2.)
so
1.80a+2.40b=21.60

Just guess and check this one

And youll get

6 of the 16 ounce and 4 of the 12 ounce

Answer 8

I think I can answer #1
eq.1 = 25+.02x
eq.2= 10 + .05x
the question is , when will eq1 equal eq.2, so you set both equations equal to each other
25+.02x=10+.05x
solving for x...
25-10=.05x-.02x
15=.03x
15/.03=x
500=x Answer =(500 cards)

Answer 9

You quite prefer to have the x extensive style on one section, and the customary extensive style on the different. think of of it like a river; the two portion of the equation is a various section. undergo in ideas, what you do on one section you should do to the different. 5x-12 = 3x+20 +12 +12 5x = 3x+32 -3x -3x 2x = 32 x = sixteen