Al saves pennies . He agrees to give 1/3 of his pennies to Bev if she would give 1/3 of what she got from Al to Carl and if Carl in turn would give 1/3 of what he got from Bev to Danni. Bev, Carl and Danni agreed and recived 9 pennies. hOW MANY PENNIES DID aL INTINALLY HAVE?
It's not clear who received 9 pennies.
Assuming Danni received 9 pennies, Carl got 9*3=27 pennies from Bev.
Therefore Bev got 3*27=81 pennies from Al.
Al had collected 81*3=243 pennies.
729
Let's solve this problem step-by-step:
Step 1: Given that Bev, Carl, and Danni received a total of 9 pennies, let's assign variables to their amounts:
- Bev received x pennies from Al.
- Carl received x/3 pennies from Bev.
- Danni received (x/3)/3 = x/9 pennies from Carl.
Step 2: We can now write the equation based on the given information:
x + x/3 + x/9 = 9
Step 3: To simplify the equation, we'll clear the fractions by multiplying the entire equation by 9:
9x + 3x + x = 9 * 9
9x + 3x + x = 81
Step 4: Combine like terms on the left side of the equation:
13x = 81
Step 5: Solve for x by dividing both sides of the equation by 13:
x = 81 / 13
Step 6: Calculate the value of x:
x ≈ 6.23
Based on this calculation, Al initially had approximately 6.23 pennies.
To find out how many pennies Al initially had, we'll work backwards step by step using the information given.
Let's assume that the number of pennies Al initially had is represented by the variable "x".
1/3 of Al's pennies are given to Bev, so Al gives (1/3)x pennies to Bev.
Bev then gives 1/3 of what she got from Al to Carl, so Bev gives (1/3)((1/3)x) = (1/9)x pennies to Carl.
Finally, Carl gives 1/3 of what he got from Bev to Danni, so Carl gives (1/3)((1/9)x) = (1/27)x pennies to Danni.
Given that Bev, Carl, and Danni received a total of 9 pennies, we can add up their individual amounts:
(1/3)x + (1/9)x + (1/27)x = 9
To simplify the equation, we can find the least common denominator of the fractions. The least common denominator for 3, 9, and 27 is 27. Multiplying each term by 27, we get:
9x + 3x + x = 27 * 9
13x = 243
Now, solve for x by dividing both sides of the equation by 13:
13x / 13 = 243 / 13
x = 18
Therefore, Al initially had 18 pennies.