Damon, the problem in the book is
5/8*t + 2/15*t = 17/20
I saw it and answered down below.
We have a fractional equation:
5/8*t + 2/15*t = 17/20
Our first goal is to find the LCD.
What is the LCD of 8, 15 and 20?
How about 120?
Yes, LCD = 120.
We now multiply each term on BOTH sides of the fractional equation by 120 to do away with ALL the fractions.
5/8(t) times 120 = 75t
2/15(t) times 120 = 16t
17/20 times 120 = 102
We now have a linear (not fractional) equation:
75t + 16t = 102
Combine like terms on the left side of the equation.
Doing so, we get this:
91t = 102
To find t, divide BOTH sides of the equation by 91 (our coefficient).
t = 102/91
Done!
To solve the equation 5/8 * t + 2/15 * t = 17/20, we need to find the value of t that satisfies this equation. Here's how you can solve it:
Step 1: Find a common denominator
To add or subtract fractions, we first need to find a common denominator. In this case, the least common multiple (LCM) of 8 and 15 is 120. So, we can rewrite the equation with the common denominator of 120:
(5/8)t + (2/15)t = (17/20)
Step 2: Multiply both sides by the common denominator
To eliminate the denominators, we can multiply both sides of the equation by 120:
120 * [(5/8)t + (2/15)t] = 120 * (17/20)
Step 3: Simplify both sides
Now, we can simplify both sides of the equation by following the distributive property:
(120*5/8)t + (120*2/15)t = (120*17/20)
Step 4: Simplify further
Let's simplify the fractions on both sides:
(600/8)t + (240/15)t = (2040/20)
Simplifying the fractions gives us:
(75/1)t + (16/1)t = (102/1)
Step 5: Combine like terms
Now, we can combine like terms on both sides of the equation:
(75t + 16t) = 102
Step 6: Solve for t
Combine the terms:
91t = 102
Divide both sides by 91 to solve for t:
t = 102/91
The solution to the equation is t = 102/91.