There were 4342 buttons in three bags, A, B and C. There were 18 more buttons in bag B than in bag A. There were 3 times as many buttons in bag C as in bag B. How many buttons were in bag A? With model drawing please
Let's start by assigning variables to the number of buttons in each bag:
Let A = number of buttons in bag A
B = number of buttons in bag B
C = number of buttons in bag C
From the given information, we can establish the following equations:
1) B = A + 18 (There were 18 more buttons in bag B than in bag A.)
2) C = 3B (There were 3 times as many buttons in bag C as in bag B.)
3) A + B + C = 4342 (Total number of buttons in all three bags is 4342.)
To solve the problem, we need to find the value of A.
Let's substitute the equations (1) and (2) into equation (3):
A + (A + 18) + 3(A + 18) = 4342
Now, let's simplify and solve for A:
A + A + 18 + 3A + 54 = 4342
5A + 72 = 4342
5A = 4270
A = 854
Therefore, there were 854 buttons in bag A.
Model Drawing:
A B C
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A B C
To solve this problem, let's break it down step by step.
Step 1: Determine the relationship between the number of buttons in bags A, B, and C.
- Let's assume that the number of buttons in bag A is denoted by the variable "x".
- Since there are 18 more buttons in bag B than in bag A, the number of buttons in bag B would be "x + 18".
- Additionally, since there are 3 times as many buttons in bag C as in bag B, the number of buttons in bag C would be "3 * (x + 18)".
Step 2: Calculate the total number of buttons.
We know that there were a total of 4342 buttons in all three bags combined, so we can set up the equation:
x + (x + 18) + 3 * (x + 18) = 4342
Step 3: Solve for x.
Let's solve the equation:
x + x + 18 + 3x + 54 = 4342
5x + 72 = 4342
5x = 4270
x = 854
Step 4: Calculate the number of buttons in bag A.
Now that we know the value of "x", we can substitute it back into the equation to find the number of buttons in bag A:
x = 854
So, there are 854 buttons in bag A.
Model Drawing:
Let's create a simple model to represent the relationship between the number of buttons in bags A, B, and C:
Bag A: x (number of buttons)
Bag B: x + 18 (number of buttons, 18 more than bag A)
Bag C: 3 * (x + 18) (number of buttons, 3 times bag B)
Put the words into algebra
a+b+c = 4342
b = a+18
c = 3b
So, a=854