Question

There were 80 apples and pears in a basket at first. 0.4 of the apples and 2/3 of the pears were eaten. In the end there were 36 fruits left. How many apples were there in the basket at fist?

Answer 1

Let's start by using algebra to solve this problem. We'll let "a" be the number of apples in the basket at first, and "p" be the number of pears. We know that:

a + p = 80 (since there were 80 fruits at first)

We also know that 0.4 of the apples were eaten, which means that 0.6 of the apples were left. Similarly, 2/3 of the pears were eaten, which means that 1/3 of the pears were left. So:

0.6a + (1/3)p = 36

Now we have two equations and two variables, which we can solve using substitution or elimination. Let's solve for "p" in the first equation:

p = 80 - a

Now we can substitute this expression for "p" in the second equation:

0.6a + (1/3)(80 - a) = 36

Multiplying both sides by 3 to get rid of the fraction:

1.8a + 26.67 - 0.33a = 36

Combining like terms:

1.47a + 26.67 = 36

Subtracting 26.67 from both sides:

1.47a = 9.33

Dividing both sides by 1.47:

a = 6.33

So there were approximately 6.33 apples in the basket at first. Since we can't have a fraction of an apple, let's round up to 7 apples. To check our answer, we can substitute this value for "a" in the first equation:

a + p = 80

7 + p = 80

Subtracting 7 from both sides:

p = 73

So there were 7 apples and 73 pears in the basket at first. We can check that 0.4 of the apples were eaten (which is 0.4 x 7 = 2.8, or 3 since we can't eat a fraction of an apple), and 2/3 of the pears were eaten (which is 2/3 x 73 = 48.67, or 49 since we can't eat a fraction of a pear). So there were 7 - 3 = 4 apples left, and 73 - 49 = 24 pears left, for a total of 28 fruits left. This doesn't match the given information that there were 36 fruits left, so there must be an error in the problem statement or our calculations.

Answer 2

Let's start by setting up an equation to solve for the number of apples in the basket at first.

Let A be the number of apples in the basket at first, and P be the number of pears in the basket at first.

From the problem, we know that:

- A + P = 80 (the total number of fruits in the basket at first)

- 0.4A (40% of the apples) and (2/3)P (66.67% of the pears) were eaten

- In the end, there were 36 fruits left, so the number of fruits that were eaten was 80 - 36 = 44.

From this information, we can set up the following equation:

0.4A + (2/3)P = 44

We can then use the first equation to solve for P in terms of A:

P = 80 - A

Substituting this into the second equation, we get:

0.4A + (2/3)(80 - A) = 44

Simplifying this equation, we get:

0.4A + 53.33 - (2/3)A = 44

Multiplying both sides by 15 to eliminate the fractions, we get:

6A + 800 - 10A = 660

Simplifying this equation, we get:

-4A = -140

Dividing both sides by -4, we get:

A = 35

Therefore, there were 35 apples in the basket at first.