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?

Question

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?

Answer 1

To solve this problem, let's use the given information and set up an equation.

We are given that the total amount of time Lisa, Beth, and Tim painted is 24 hours.

Let's say Lisa painted for x hours. According to the given information, Beth painted 1 3 5 times the amount Lisa painted. So, Beth painted 1 3 5 * x hours. Similarly, Tim painted 1 2 3 times the amount Lisa painted, so Tim painted 1 2 3 * x hours.

Now, we can set up an equation to represent the total amount of time painted:

x + 1 3 5x + 1 2 3x = 24

To solve this equation, we need to combine like terms:

x + 1 3 5x + 1 2 3x = 24
x + 5 6 5x = 24

To add the terms with x, we need to have common denominators. The least common denominator of 1, 3, and 5 is 15:

15x + (5 6 5x) = 24

Simplifying further:

15x + 5 6 5x = 24
15x + (5 6 5/1)x = 24

Now, to combine the terms with x, we can multiply each term by their respective denominators:

15x + (5 6 5/1)x = 24
15x + (5/1 * 6/5 * 5/1)x = 24
15x + (5 6 5)x = 24

Now, let's add the terms with x:

15x + (5 6 5)x = 24
15x + 933x = 24

Combining like terms:

15x + 933x = 24
(15 + 933)x = 24
948x = 24

To solve for x, we need to isolate x by dividing both sides of the equation by 948:

948x = 24
x = 24/948

Simplifying the fraction:

x = 1/79

Therefore, the amount of time painted by Lisa, represented by x, is 1/79 of an hour.

Answer 2

Let's first solve the equation to find the value of x. We know that the amount of time Beth painted is 1 3 5 times the amount Lisa painted. So, the equation will be:

Beth's time = 1 3 5 * Lisa's time

Similarly, we know that the amount of time Tim painted is 1 2 3 times the amount Lisa painted. So, the equation for Tim's time will be:

Tim's time = 1 2 3 * Lisa's time

Since the total time painted is 24 hours, we can write another equation:

Lisa's time + Beth's time + Tim's time = 24

Now let's substitute the values of Beth's and Tim's time in terms of Lisa's time in the third equation:

Lisa's time + (1 3 5 * Lisa's time) + (1 2 3 * Lisa's time) = 24

Simplifying the equation:

Lisa's time + (15/5 * Lisa's time) + (6/3 * Lisa's time) = 24

Combining like terms:

Lisa's time + 3 * Lisa's time + 2 * Lisa's time = 24

Simplifying further:

6 * Lisa's time = 24

Now, divide both sides of the equation by 6:

Lisa's time = 24/6

Lisa's time = 4

Therefore, x, the amount of time painted by Lisa, is 4 hours.

Answer 3

Lisa+Beth+Time=24

x+135x+123x=24
add the left side up
259x=24
x= 24/259 hours which is not very long