Answer:
1. 18x + 35y = 598
x + y = 20
Isolate a variable in the second equation:
y = -x + 20
Plug y back into the first equation
18x + 35(-x + 20) = 598
18x - 35x + 700 = 598
-17x +700 = 598
-17x = -102
x = 6
You carpool 6 days of the 20
6 + y = 20
y = 14
You ride the bus 14 days of the 20
2. 4.50n + 3p = 252
p = 2n
Substitute p into the first equation
4.50n + 3(2n) = 252
4.50n + 6n = 252
10.5n = 252
n = 24
They sold 24 cans of nuts
p = 2(24)
p = 48
They sold 48 boxes of popcorn
The group sold, in total, 24 + 48 = 72 cans of nuts and boxes of popcorn.
3. x - y = 3
x + y = 8
Isolate a variable
x = y + 3
(y + 3) + y = 8
2y + 3 = 8
2y = 5
y = 2.5
The average speed with wind is 2.5 mph
x - 2.5 = 3
x = 5.5
The average speed without wind is 5.5mph
4. x + 8y = 22.8
x + 6y = 18.6
Isolate
x = -8y + 22.8
Substitute
(-8y + 22.8) + 6y = 18.6
-2y + 22.8 = 18.6
-2y = -4.2
y = -2.1
The gas costs $2.10 per gallon
x + 8(2.1) = 22.8
x + 16.8 = 22.8
x = 6
The cost of the car was is $6.
5. Cost = 9.99 + 2.49x
Cost = 20.49 + 1.79x
To find which one is better, we need to set them equal to each other at first.
9.99 + 2.49x = 20.49 + 1.79x
9.99 + 0.70x = 20.49
0.70x = 10.5
x = 15
So, they cost the same at 15 rentals.
To find which one is the better deal let's see how much both cost after 16 rentals.
Cost = 9.99 + 2.49(16)
= 49.83
Cost = 20.49 + 1.79(16)
= 49.13
Therefore, Main Street is the better deal because after the equilibrium Main Street costs less than Big Video.
6. x + y = 15
.25x + .05y = 2.75
Isolate
x = -y + 15
Solve
.25(-y + 15) + .05y = 2.75
-.25y + 3.75 + .05y = 2.75
-0.2y + 3.75 = 2.75
-0.2y = -1
y = 5
There are 5 nickels
x + 5 = 15
x = 10
There are 10 quarters
7. x + y = 26
x + .25y = 17
Isolate
x = -y + 26
Substitute
(-y + 26) + .25y = 17
-0.75y + 26 = 17
-0.75y = -9
y = 12
There are 12 quarters in his pocket
x + 12 = 26
x = 14
There are 14 dollars
I hope this helps!!
- Kay :)