10+ 10 + s = 180
5a + 3c + 2s = 500
a = 10c
See previous.
To solve this system of equations, we will use the method of substitution. First, we will start by solving the third equation for "a" in terms of "c".
Given: a = 10c
Next, we will substitute this expression for "a" in the second equation and solve for "s".
5(10c) + 3c + 2s = 500
50c + 3c + 2s = 500
53c + 2s = 500
2s = 500 - 53c
2s = 500 - 53c
Now, we will substitute the value of "s" from the above equation into the first equation and solve for "c".
10 + 10 + (500 - 53c) = 180
20 + 500 - 53c = 180
520 - 53c = 180
-53c = -340
c = -340 / -53
c = 6.42 (rounded to two decimal places)
To find the value of "a", substitute the value of "c" back into the third equation.
a = 10c
a = 10(6.42)
a = 64.2 (rounded to one decimal place)
Finally, to find the value of "s", substitute the values of "a" and "c" into the second equation.
5a + 3c + 2s = 500
5(64.2) + 3(6.42) + 2s = 500
321 + 19.26 + 2s = 500
2s = 500 - 321 - 19.26
2s = 179.74
s = 179.74 / 2
s = 89.87 (rounded to two decimal places)
Therefore, the solution to the system of equations is:
a = 64.2, c = 6.42, and s = 89.87.