You must translate the words into a system of equations for solving the problem.
Solve the system of equations for the answers. You must provide detailed step-by-step explanations on how you solved the problem.
Explain in detail how you would check your answers.
Answer:
x = 47
y = 94
Step-by-step explanation:
Givens
Let the larger number = y Note: y must be even. Why is that?
Let the smaller number = x
Equations
x = 1/2 y
x + y = 141
Solution
Substitute x from the first equation into the second equation
1/2 y + y = 141
Change 1/2 y to 0.5y
0.5y + y = 141
Combine the left
1.5y = 141
Divide both sides by 1.5
1.5y/1.5 = 141/1.5
Do the division
y = 94 And y is even.
================
x = 1/2y
x = 1/2*94
x = 47
Check
The smaller number is 1/2 the larger one This is correct.
47 + 94 = 141 and this also checks.
Answer:
x = 47
y = 94
Step-by-step explanation:
We know that one number is half another number and the sum of these two numbers is 141. We are to find the numbers.
Assuming and to be the numbers, we can write it as:
--- (1)
--- (2)
Substituting the value of from (1) into (2) to get:
y = 94
Now substituting this value of in (1):
x = 47
Translating it in other words:
One number is double the other number and the sum of the two number is 141.
Checking answers:
Answer:
16x + 13
Step-by-step explanation:
(4x + 11) + (12x + 2)
combine like terms (add the x's and add the numbers)
4x + 12x = 16x
11 + 2 = 13
(4x + 11) + (12x + 2) =
16x + 13
Divide the total the lake holds by the number of days:
400 million / 25 days = 16 million gallons per day.
The maximum rate of drainage, in millions of gallons per day is 16 millions of gallons per day.
A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Amount of water reservoir can hold = 400400400 million gallons of water ≈ million gallons
Estimated days will drainage take = 252525 days ≈ days
Then the maximum rate of drainage, in millions of gallons per day is
⇒
⇒
Hence we can conclude that the maximum rate of drainage, in millions of gallons per day is 16 millions of gallons per day.
Learn more about word problems here
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