Henry had to paint some cartons. On the first day, the number of cartons he painted was 40% of the number of cartons that he had not painted. One week later, he painted another 100 cartons. As a result, the total number of painted cartons became 28 more than 1/2 of the total number of cartons. How many more cartons were unpainted than painted on the first day?

Question

Henry had to paint some cartons. On the first day, the number of cartons he painted was 40% of the number of cartons that he had not painted. One week later, he painted another 100 cartons. As a result, the total number of painted cartons became 28 more than 1/2 of the total number of cartons. How many more cartons were unpainted than painted on the first day?

Answer 1

Let no. of Carton painted on first day = x.

no. of unpainted carton on first day = y
x = 40% of 8y = 40/100 * y = 0.4y
x = 0.4y — (1)
One week later, painted cartons = 100.
=> x + 100 = 28 + 1/2 (x + y) — (2)
Sub (1) in (2)
0.4y + 100 = 28 + 1/2 (y + 0.4y)
0.4y = 28 - 100 + 0.5y + 0.2y
(0.4 - 0.5 - 0.2)y = -72
-0.3y = -72 => y = 72/0.3
y = 240
x = 0.4 * 240 = 96
No. of painting cartons (1st day) = 96
No. of unpainted cartons = 240
Difference = 240 - 96 = 144
Answer = 144

Answer 2

Let's start by assigning variables to the unknowns in the problem:

Let's say the total number of cartons that Henry had initially is 'x'.
Let's say the number of cartons that Henry painted on the first day is 'y'.
We know that y = 0.4 * (x - y) (he painted 40% of the cartons he had not painted)
Similarly, on the second day, Henry painted 100 cartons. So, the number of cartons painted on the second day is 100.
The total number of painted cartons after a week is y + 100.
The total number of cartons is x.
According to the problem, y + 100 = (1/2) * x + 28 (the total number of painted cartons is 28 more than half of the total number of cartons)

Let's solve these two equations to find the values of x and y.

Answer 3

To solve this problem, we need to break it down step by step.

Let's start by figuring out the number of cartons Henry painted on the first day. We are given that the number of cartons he painted on the first day was 40% of the number of cartons he had not painted. This can be represented as:

Cartons painted on the first day = 40% * (Cartons not painted on the first day)

Now, let's assume the total number of cartons is "x." This means the number of cartons painted on the first day is 40% of (x - Cartons painted on the first day). Simplifying this equation gives us:

Cartons painted on the first day = 0.4 * (x - Cartons painted on the first day)

Next, we are told that one week later, Henry painted another 100 cartons. Therefore, the new total number of painted cartons is Cartons painted on the first day + 100.

Now, the total number of painted cartons became 28 more than half of the total number of cartons. This can be represented as:

Total painted cartons = (1/2) * Total cartons + 28

Since we know that the total number of painted cartons is Cartons painted on the first day + 100, we can substitute this into the equation:

Cartons painted on the first day + 100 = (1/2) * Total cartons + 28

Simplifying this equation gives us:

Cartons painted on the first day + 72 = (1/2) * Total cartons

Now we can solve these two equations simultaneously to find the values of Cartons painted on the first day and Total cartons.

1) Cartons painted on the first day = 0.4 * (x - Cartons painted on the first day)
2) Cartons painted on the first day + 72 = (1/2) * Total cartons

Solving these equations will give us the values we need.

Please note that this solution assumes the number of cartons painted on the first day and the total number of cartons remains constant during the week.