In the Apollo spacecraft, the service module weighed 3000 lbs less than 5 times the weight of the command module.The lunar module weighed 1000 lbs less than 3 times the weight of the command module.If the total weight of the three modules was 95000 lbs, how much did each weigh?I need help finishing the problem.
s=3000-5c l=1000-3c l+c+s=95000
1,000-3c+c+3000-5c=95000
1,000+-7=95,000
Why use all those variables?
let the weight of the command module be x
now just translate the given English into Math
"the service module weighed 3000 lbs less than 5 times the weight of the command module"
---> sm = 5x-3000
"The lunar module weighed 1000 lbs less than 3 times the weight of the command module"
sm = 3x-1000
"If the total weight of the three modules was 95000 lbs"
---> x + 5x-3000 + 3x-1000 = 95000
notice only one variable,
solve for x
sub back into my definitions.
To solve the problem, you need to substitute the values of the service module (s) and the lunar module (l) in terms of the command module (c) into the third equation.
From the given information, you have:
s = 3000 - 5c
l = 1000 - 3c
Now substitute these values into the equation:
l + c + s = 95000
(1000 - 3c) + c + (3000 - 5c) = 95000
Now combine like terms:
1000 - 3c + c + 3000 - 5c = 95000
Combine similar terms on the left side:
-7c + 4000 = 95000
Next, isolate the variable:
-7c = 95000 - 4000
Simplify:
-7c = 91000
Finally, solve for c by dividing both sides by -7:
c = 91000 / -7
Now you can calculate the value of c.