Help with my algebra math homework! on systems of equation. please help me!!?

Question

There is a total of 160 vehicles, made up of cars and trucks. There is a total mass of 182,800 kilograms of vehicles, and each truck is 1400 kg and each car is 1000 kg. How many kind of each kind are there?

How can I solve this problem? Details please!

Answer 1

Let c = # of cars
t = # of trucks

Then c + t = 160 (there are 160 vehicles altogether)

Since each car weighs 1000 and each truck weighs 1400,
1000c + 1400t = 182800 (total mass of 182,800).

Two equations, two unknowns:

c + t = 160
1000c + 1400t = 182800

Use substitution to solve. From the first equation, since
c + t = 160, then c = 160 - t. Substitute this into the second equation, and then solve for t.

1000 [160 - t] + 1400t = 182800

Distribute the 1000,

160000 - 1000t + 1400t = 182800
160000 + 400t = 182800
400t = 182800 - 160000
400t = 22800
t = 22800/400
t = 57

Now that we have t, we can get c.
c = 160 - t
c = 160 - 57
c = 103

t = 57, c = 103
There are 57 cars and 103 trucks.

**Edited due to arithmetic error proven by answerers above**

Answer 2

you're right to set it up as a system of eqations.

let c represent cars and t represent trucks. since you know that the total number of cars and trucks are 160, you can say:

c + t = 160

since you also know the total mass is 182,800kg and the weight of each truck is 1400kg and mass of each car is 1000kg, you can set up the following equation:

1000*c + 1400*t = 182800

now, solve the first equation for either c or t. *I'll solve for c*
c = 160 - t
now, substitue this in for the c in the second equation.

1000*(160-t) + 1400*t = 182800
160,000 - 1000*t + 1400*t = 182800
solve for t
400*t = 182800-160000
400*t = 22800
t = 22800/400
t = 57

now, putting this in to the first equation
c + 57 = 160
c = 160 - 57
c = 103

so, there are 103 cars and 57 trucks.

hope my explanation helped.

Answer 3

I used to hate these type of problems back when I took algebra!

Anyways, I try to help you the best I can.

x=amount of cars
y=amount of trucks

so that means x+y=160
and 1400y+1000x=182800

if you change the first equation to x=160-y, you can then subsitute it into the other equation, to get:
1400y+1000(160-y)=182800
1400y+160000-1000y=182800
400y+160000=182800
400y=22800
y=57

Now that you know how many trucks there are, plug 57 into the first equation so that you have x+57=160. From there just using simple alebra you can solve for the amount of cars, which is 103.

So x=103 and y=57. Hope I helped.

Answer 4

You must set up a very simple equation to resolve the problem. First let:
#of cars = x
# of trucks = 160 - x

Since you know the masses of cars and trucks add up to 182,800 you can write it as:

(x)(1000) + (160 - x)(1400) = 182800

1000x +224000 - 1400x = 182800

-400x = -41200

x = 103

Since x = 103, there are 103 cars and (160 - x) = 57 trucks

103 cars
57 trucks

Hope that helps :)

Answer 5

Let x = number of cars
Then 160 - x = number of trucks
1000x + 1400(160-x) = 182,800
1000x + 224,000 - 1400 x = 182,800
-400x = 182,800-224,000 = - 41,200
x= 103 = number of cars
160-x = 57 = number of trucks

Answer 6

let truck be x
let car be y
then you have two equations:
1400 X + 1000 Y = 182800
X + Y = 160
I hope you can take it from here!
(hint: you need either all X or all Y, multiply the second equation so the X or the Y cancels out!)

Answer 7

ok....
suppose u have anumber of cars = x
and a number of trucks = y
and we have a total of 160 vehicle..so
number of cars + number of trucks = 160
x + y = 160......equation 1

total mass of cars = number of cars * mass of a car = x * 1,000 = 1,000x
total mass of trucks = number of trucks * mass of a truck = y * 1,400 = 1,400y
and we have a total mass of 182,800 kg
total mass of cars + total mass of trucks = 182,800
1,000x + 1,400 y = 182,800..........equation 2



now we have to solve equation 1 & equation 2 simulatinously (together)

x + y = 160..............multiply * - 1,400 to remove y's
1,000x + 1,400 y = 182,800
_______________________
- 1,400 x - 1,400 y = -224,000
1,000x + 1,400 y = 182,800
________________________add both equations
-400x = - 41,200
x = -41,200 / -400
x = 103

to get y put x = 103 at the first or the second equation
x + y = 160
103 + y = 160
y = 160 - 103
y = 57

so there are 103 cars & 57 trucks

I hope this helps..

Answer 8

Let: x=the number of cars and y=the number of trucks
x+y=160------------------------->5x+5y=800 (1)
1000x+1400y=182,800 ---> 5x+7y=914 (2)
Subtract equation (2) to (1) and we get:
2y=114--->y=57
x=160-57=103
Therefore, there are 103 cars and 57 trucks

Answer 9

xC + yT = 160
xC1000 + yT1400 = 182800
-1000xC - 1000yT = -160000
0 + 400yT = 22800
yT = 22800/400 = 57T
160 - 57 = 103C

Check:
57*1,400 + 103*1,000 = 182,800 Checks

57 Trucks + 103 cars

Answer 10

c+t = 160
1000c + 1400t = 182800
subtract `1000 times first from second
400 t = 22800
so t = 57
so c = 103