Lisa, Beth, and Tim painted their grandparent's house.
• The amount of time Lisa painted can be represented by x.
• The amount of time Beth painted is 1 3/5 times the amount Lisa painted
• The amount of time Tim painted is 1 2/3 times the amount Lisa painted.
• The total amount of time Lisa, Beth, and Tim painted is 24 hours.
What is x, the amount of time painted by Lisa?
Oh this isn't trigonometry my first name is very long so my nickname is trig
To find the amount of time Lisa painted, we need to assign a variable to represent her time. Let's say that x represents the amount of time Lisa painted.
According to the given information:
- The amount of time Beth painted is 1 3/5 times the amount Lisa painted.
This means that Beth painted (1 3/5) * x hours.
- The amount of time Tim painted is 1 2/3 times the amount Lisa painted.
This means that Tim painted (1 2/3) * x hours.
The total amount of time Lisa, Beth, and Tim painted is 24 hours.
So we can write the equation:
x + (1 3/5) * x + (1 2/3) * x = 24
Now let's solve this equation to find the value of x.
First, let's convert the mixed fractions to improper fractions:
(1 3/5) = 8/5 (1 2/3) = 5/3
Now our equation becomes:
x + (8/5) * x + (5/3) * x = 24
Next, let's find the least common denominator (LCD) of the fractions, which is 15:
x + (8/5) * x + (5/3) * x = 24
To get rid of the fractions, we multiply every term by 15:
15*x + 15*(8/5)*x + 15*(5/3)*x = 24*15
Now let's simplify the equation:
15x + 24x + 25x = 360
Combine like terms:
64x = 360
Divide both sides of the equation by 64 to solve for x:
x = 360/64
Simplify the fraction:
x = 5.625
Therefore, the amount of time painted by Lisa (represented by x) is 5.625 hours.
How is this Trig ???
anyway
Lisa --- x
Beth ---- (8/5)x
Tim --- (5/3)x
x + (8/5)x + (5/3)x = 24
multiply by 15 , the LCD
15x + 24x + 25x = 360
Now it becomes very easy to solve for x