If 1/2 of a number, 1/3 of the number, 1/4 of the number, and 2/7 of the number are added together, the sum is 575. What is the number? Please show steps/work.
n(1/2 + 1/3 + 1/4 + 2/7) = 575
115/84 n = 575 = 5*115
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To find the number, let's break down the problem into steps:
Step 1: Assign a variable
Let's assign a variable to represent the number. We'll call it "x".
Step 2: Set up equations
We are given that 1/2 of the number + 1/3 of the number + 1/4 of the number + 2/7 of the number equals 575. We can write this as an equation:
(1/2)x + (1/3)x + (1/4)x + (2/7)x = 575
Step 3: Solve the equation
To solve this equation, we need to get rid of the fractions. We can do this by finding the least common denominator (LCD) of the fractions, which in this case is 84.
We need to multiply each term by the appropriate factor to eliminate the denominators. Multiplying by 84 will clear all the denominators:
84 * (1/2)x + 84 * (1/3)x + 84 * (1/4)x + 84 * (2/7)x = 575
Simplifying this equation gives us:
42x + 28x + 21x + 48x = 575 * 84
Simplifying further:
139x = 575 * 84
Step 4: Solve for x
To isolate x, we will divide both sides of the equation by 139:
x = (575 * 84) / 139
Evaluating this expression will give us the value of x, which is the number you are looking for.