Can anyone show me how to solve this?
.1g+3.75m=7.36 and 8.2g+21m=73 Thank you
.1g+3.75m=7.36
8.2g+21m=73
method of determinates
D= .1*21-8.2*3.75 figure that.
m= (.1*73-8.2*7.36)/D figure that.
g= (7.36*21-73*3.75)/D figure that
I'm sorry but this does not help. WHat is D?
I usually get rid of nasty decimals ...
.1g+3.75m=7.36 --> 10g + 375m = 736 --> g = (736-375m)/10
8.2g+21m=73 ----> 82g + 210m = 730
10g +375m = 736 -times 410 --> 4100g + 153750m = 301760
82g + 210m = 730 -times 50 --> 4100g + 10500m = 36500
subtract them:
143250m = 265260
m = 265260/143250 = 8842/4775
sub into 82g + 210m = 730
82g + 210(8842/4775) = 730
...
g = 3973/955
Thanks alot Reiny that was super helpful. I have a math test tomrrow!
Certainly! To solve this system of equations:
1. Start by writing the two equations:
Equation 1: 0.1g + 3.75m = 7.36
Equation 2: 8.2g + 21m = 73
2. Choose a method to solve the system of equations. In this case, we'll use the method of substitution.
3. Solve one equation for one variable. Let's solve Equation 1 for g:
0.1g + 3.75m = 7.36
0.1g = 7.36 - 3.75m
g = (7.36 - 3.75m) / 0.1
4. Substitute g in Equation 2 with the expression we just found:
8.2((7.36 - 3.75m) / 0.1) + 21m = 73
5. Simplify the equation:
(82(7.36 - 3.75m) + 210m) / 10 = 73
(60.32 - 30.75m + 210m) / 10 = 73
(60.32 + 179.25m) / 10 = 73
6. Solve for m by isolating the variable:
60.32 + 179.25m = 730
179.25m = 730 - 60.32
179.25m = 669.68
m = 669.68 / 179.25
7. Calculate m:
m ≈ 3.7395
8. Substitute the value of m into Equation 1 to solve for g:
0.1g + 3.75(3.7395) = 7.36
0.1g + 14.048125 = 7.36
0.1g = 7.36 - 14.048125
0.1g = -6.688125
g = -6.688125 / 0.1
9. Calculate g:
g ≈ -66.88125
So the values of g and m that solve the system of equations are g ≈ -66.88125 and m ≈ 3.7395.