Sam makes some read rolls. He gives 2/5 of the bread rolls to his neighbor and 4/9 of the remainder to his cousin. He has 15 bread rolls left. How many bread rolls does Sam make?
Well, it seems like Sam is quite the bread enthusiast! Let's do some math to figure out how many bread rolls he initially made.
First, we know that Sam gave 2/5 of the bread rolls to his neighbor. This means he had 3/5 of the original amount left.
Next, we're told that Sam gave 4/9 of the remaining rolls to his cousin. So, he had 5/9 of the 3/5 left.
To find out how many rolls Sam initially made, let's set up an equation: (5/9) * (3/5) * x = 15.
Now, solving for x:
(5/9) * (3/5) * x = 15
(15/45) * x = 15
(1/3) * x = 15
x = 15 * 3
x = 45
Ta-da! Sam initially made 45 bread rolls. That's a lot of dough!
To find out how many bread rolls Sam made, let's break down the information given:
1. Sam gives 2/5 of the bread rolls to his neighbor.
2. After giving the rolls to his neighbor, he has a remainder.
3. Sam gives 4/9 of the remainder to his cousin.
4. After giving rolls to his cousin, he has 15 bread rolls left.
Let's work through the problem step by step:
Step 1: Sam gives 2/5 of the bread rolls to his neighbor.
Let's represent the total number of bread rolls Sam made as "x". Since Sam gives 2/5 of x to his neighbor, the neighbor receives 2/5 * x bread rolls. This means the remainder that Sam has after giving some rolls to his neighbor is (1 - 2/5) * x.
Step 2: After giving rolls to his neighbor, Sam has a remainder.
The remainder Sam has after giving some rolls to his neighbor is (1 - 2/5) * x. Let's represent the remainder as "y".
Step 3: Sam gives 4/9 of the remainder to his cousin.
Sam gives 4/9 of y to his cousin. This means his cousin receives 4/9 * y bread rolls. The remaining rolls Sam has after giving some to his cousin can be calculated as (1 - 4/9) * y.
Step 4: After giving rolls to his cousin, Sam has 15 bread rolls left.
The remaining rolls Sam has after giving some to his cousin can be calculated as (1 - 4/9) * y, and we know that this is equal to 15. So we have the equation (1 - 4/9) * y = 15.
To find the value of x (the total number of bread rolls Sam made), we need to solve for y using the equation derived in Step 4.
Let the no. of bread rolls be x.
Neighbor: 2/5(x)
Remainder = x - 2/5(x) = 3/5(x)
Cousin = 4/9 * 3/5(x) = 4/15(x)
x - 2/5(x) - 4/15(x) = 15
x - 6/15(x) - 4/15(x) = 15
x - 10/15(x) = 15
(15x - 10x) = 225
5x = 225
x = 225/5 = 45
Therefore, he made 45 rolls.