are you good at math?

Question

ok i need help explaing this:

s rentsl car agency charges $13 per day plus 15 cents per mile to rent a certain car, while another agency charges 17 per day plus 9 cents per mile to rent. how many miles will have to be driven for the cost of the two agencies to match?

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he modern grocery has cashews that sell for $4.50 a pound and penuts for $2.50 per pounds . how much of each must albert , the grocer mix to ge 80 pounds of mixture, that he can sell for $3.00 per pound? expres the problem in any linear equation

Answer 1

First one - 13+.15x = 17+.09x
.15x = 4+.09x
.06x=4
x=66.67

so if each car drives 66.67 miles they'll match

No clue on the second one...

Answer 2

Answer 1:
Let the number of miles driven be x
Convert everything to cents and calculate. The required equation is:

1300 + 15x = 1700 + 9x
6x + 1300 = 1700
6x = 400
x = 400/6 = 200/3 = 66.67 approx

66.67 approximate miles must be driven for the charges to match.

Answer 2:
Let the no. of pounds of cashews be x and that of peanuts be y.
4.50x + 2.50y = 3*80
4.50x + 2.50y = 240
450x + 250y = 24000
50(9x + 5y) = 24000
9x + 5y = 480 ..... (1)

x + y = 80 .... (2)
x = 80 - y ... (3)

Put (3) in (1)
9(80 - y) + 5y = 480
720 - 9y + 5y = 480
-4y = -240
y = 60.........(4)

Put (4) in (3)
x = 80 - 60
x = 20

There are 20 pounds of cashews and 60 pounds of peanuts in the mixture

Answer 3

First, figure out how much more the second company charges per day than the first. 17-13 is 4. So to make them equal, you have to drive more miles to equal $4. So do $4 divided by $0.15. It is 26.67 (6 repeating) miles per day to make them equal.

Second.
2 equations (x is cashews, y is peanuts):
($4.50x+2.50y)/(80)=3--This adds the cost of the pounds of cashews, plus the cost of the pounds of peanuts, then divides by the total weight to get the average cost, which must be 3.00
x+y=80--this is the 2 weights added together, which must equal 80

Solve using elimination, substitution, or graphing, and you get
x=20
y=60

Answer 4

First question:
1. Set the words into numbers like this (using cents only):
1300 + 15m = 1700 + 9m

2. subtract 1300 from both sides:
15m = 400 + 9m

3. subtract 9m from both sides
6m = 400

4. divide both sides by 6
m = 66.67 miles

Second question:
1. Set the words into numbers like this, with two equations:

(first equation) c + p = 80 (weight of cashews and peanuts)
so
c = 80 - p

(second equation) 4.5*c + 2.5*p = 3*80

2. We already know that c = 80-p, so we can substitute this expression of c into equation 2.

4.5 * (80-p) + 2.5p = 3*80

3. Now simplify:

360 - 4.5p + 2.5p = 240
360 - 2p = 240
120 - 2p = 0
2p = 120
p = 60

4. Back to equation 1: c+p=80
so
c = 20

Answer 5

First problem has already been solved by fellows.
I attempt the second one. Let x pound of cashews & y pound of penuts are mixed, then
x + y = 80 ---- Equation (1)
4.5x + 2.5y = 80*3, i.e., 4.5x + 2.5y = 240, i.e., 9x + 5y = 480 ---Eq.(2)

from (1) y = 80-x
put this value of y in (2)
9x + 400-5x = 480
4x = 80
x = 20 pound
so y = 60 pound.

Answer 6

13x+15x=17x+9x
28x=26x
13 miles

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4.50x+2.50(80)=3(x+80)