Bob planted some lettuce seedlings in his garden. After a few days, one-tenth of these seedlings had been eaten by rabbits. A week later , one-fifth of the remaining seedlings had been eaten, leaving 36 seedlings unharmaed. How many seedlings had Bob planted originally?
Let x = original seedlings
x - .1x - .2(x-.1x) = 36
Solve for x.
Let's solve this step-by-step:
Step 1: Let's assume the number of seedlings Bob planted originally as 'x'.
Step 2: After a few days, one-tenth (1/10) of the seedlings had been eaten by rabbits. So, the number of seedlings remaining is (x - x/10) = (9x/10).
Step 3: A week later, one-fifth (1/5) of the remaining seedlings had been eaten. So, the number of remaining seedlings now is (9x/10 - (9x/10)/5) = 36.
Step 4: Simplifying the equation (9x/10 - (9x/10)/5) = 36:
Multiplying through by 10 to clear the fraction: 9x - (9x/5) = 360.
Multiplying through by 5 to eliminate the fraction: 45x - 9x = 1800.
Simplifying the equation: 36x = 1800.
Step 5: Solving for x:
Dividing both sides of the equation by 36: x = 1800 / 36.
Calculating: x = 50.
Therefore, Bob planted originally 50 seedlings in his garden.
To find the number of seedlings that Bob originally planted, we need to work backwards from the information given.
Let's assume that Bob originally planted x seedlings.
After a few days, one-tenth of these seedlings had been eaten by rabbits, which means (1/10)x seedlings were eaten. So the number of seedlings remaining was x - (1/10)x = (9/10)x.
A week later, one-fifth of the remaining seedlings had been eaten, which means (1/5)(9/10)x = (9/50)x seedlings were eaten. The number of seedlings remaining now is (9/10)x - (9/50)x.
According to the problem, 36 seedlings were unharmed. So the equation becomes:
(9/10)x - (9/50)x = 36
To solve this equation, we can first find a common denominator for the fractions:
(45/50)x - (9/50)x = 36
Combining the two terms on the left side, we get:
(36/50)x = 36
Now multiply both sides of the equation by the reciprocal of (36/50) to solve for x:
x = 36 * (50/36)
Simplifying this expression:
x = 50
Therefore, Bob originally planted 50 seedlings in his garden.