There are some caps in a box. 1/6 of them are red, 1/3 of them are blue and 3/7 of the remainder are green. If there are 27 green caps, how many caps are there altogether?
How should I solve this?
1/6 + 2/6 = 3/6 = 1/2 are red or blue
the other half
3/7 (1/2) = 3/14 are green
so
3/14 x = 27
1/14 x = 9
x = 14*9 =
2321
To solve this problem, you can follow these steps:
Step 1: Determine the number of green caps. Given that 3/7 of the remainder (after red and blue caps) are green, and there are 27 green caps, you can set up the equation: (3/7) * remainder = 27.
Step 2: Find the remainder of the caps. To find the remainder, subtract the number of green caps from the total number of caps: remainder = total - 27.
Step 3: Calculate the number of red caps. Given that 1/6 of the caps are red, you can set up the equation: (1/6) * total = red caps.
Step 4: Calculate the number of blue caps. Given that 1/3 of the caps are blue, you can set up the equation: (1/3) * total = blue caps.
Step 5: Determine the total number of caps. Add up the number of red, blue, and green caps: total = red caps + blue caps + 27.
Step 6: Substitute the values back into the equations to solve for the total number of caps.
Alternatively, you can solve this problem by setting up a system of equations and solving them simultaneously.
To solve this problem, you need to follow a step-by-step approach. Here's how you can do it:
Step 1: Start by finding the number of green caps in relation to the total number of caps in the box.
You are given that 3/7 of the remainder after red and blue caps are accounted for are green. Let's call the total number of caps in the box "x". Since 1/6 of the caps are red and 1/3 are blue, the remaining fraction is 1 - (1/6 + 1/3) = 1 - 1/2 = 1/2.
Therefore, 3/7 * (1/2)x = 27.
Step 2: Solve the equation for x.
To isolate x, multiply both sides of the equation by 2/7:
(3/7) * (1/2) * x = 27 * (2/7).
Simplify:
(3/14) * x = 54/7.
To get rid of the fraction, multiply both sides of the equation by the reciprocal: 14/3.
[(3/14) * x] * (14/3) = (54/7) * (14/3).
Simplify:
x = 108/7.
Step 3: Find the total number of caps.
To find the total number of caps, substitute x into the equation:
x = 108/7.
Since the problem asks for the total number of caps, and x is given as a fraction, round the answer up to the nearest whole number:
x ≈ 15.43.
Therefore, there are approximately 15 caps altogether.