Question
I thought of a number, multiplied it by 2 1/2, divided the result by 1 1/5, subtracted 7/18 from it, and got 1 5/6. What was my original number?
Answers
GPT 3.5
Let's represent the original number as x.
According to the given information, the steps are as follows:
1. Multiply by 2 1/2: 2 1/2 is equal to 5/2, so (x * 5/2).
2. Divide by 1 1/5: 1 1/5 is equal to 6/5, so [(x * 5/2) ÷ (6/5)].
3. Subtract 7/18: [(x * 5/2) ÷ (6/5)] - 7/18 = 1 5/6.
To simplify, we need to convert the mixed number 1 5/6 into an improper fraction, which is 11/6.
So, (x * 5/2) ÷ (6/5) - 7/18 = 11/6.
To get rid of the fractions, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators of the fractions, which is 90.
90 * [(x * 5/2) ÷ (6/5)] - 90 * (7/18) = 90 * (11/6).
Simplifying further gives:
45x/6 - 35/2 = 165/3.
Multiplying both sides by 6 to eliminate the fraction:
45x - 105 = 330.
Adding 105 to both sides:
45x = 435.
Dividing both sides by 45:
x = 435/45.
Therefore, the original number is x = 9.
According to the given information, the steps are as follows:
1. Multiply by 2 1/2: 2 1/2 is equal to 5/2, so (x * 5/2).
2. Divide by 1 1/5: 1 1/5 is equal to 6/5, so [(x * 5/2) ÷ (6/5)].
3. Subtract 7/18: [(x * 5/2) ÷ (6/5)] - 7/18 = 1 5/6.
To simplify, we need to convert the mixed number 1 5/6 into an improper fraction, which is 11/6.
So, (x * 5/2) ÷ (6/5) - 7/18 = 11/6.
To get rid of the fractions, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators of the fractions, which is 90.
90 * [(x * 5/2) ÷ (6/5)] - 90 * (7/18) = 90 * (11/6).
Simplifying further gives:
45x/6 - 35/2 = 165/3.
Multiplying both sides by 6 to eliminate the fraction:
45x - 105 = 330.
Adding 105 to both sides:
45x = 435.
Dividing both sides by 45:
x = 435/45.
Therefore, the original number is x = 9.
NO
GPT 3.5
Apologies for any confusion. Let's go through the steps again to find the correct answer.
1. Multiply the original number by 2 1/2: This is equivalent to multiplying it by 5/2, so we have (x * 5/2).
2. Divide the previous result by 1 1/5: This is the same as dividing by 6/5, so now we have [(x * 5/2) ÷ (6/5)].
3. Subtract 7/18: [(x * 5/2) ÷ (6/5)] - 7/18 = 1 5/6 (or 11/6).
To eliminate fractions, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 90.
90 * [(x * 5/2) ÷ (6/5)] - 90 * (7/18) = 90 * (11/6).
Simplifying further:
45x - 35 = 165.
Adding 35 to both sides:
45x = 200.
Dividing both sides by 45:
x = 200/45.
Therefore, the original number is x = 40/9 or approximately 4.44 when rounded to two decimal places.
1. Multiply the original number by 2 1/2: This is equivalent to multiplying it by 5/2, so we have (x * 5/2).
2. Divide the previous result by 1 1/5: This is the same as dividing by 6/5, so now we have [(x * 5/2) ÷ (6/5)].
3. Subtract 7/18: [(x * 5/2) ÷ (6/5)] - 7/18 = 1 5/6 (or 11/6).
To eliminate fractions, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 90.
90 * [(x * 5/2) ÷ (6/5)] - 90 * (7/18) = 90 * (11/6).
Simplifying further:
45x - 35 = 165.
Adding 35 to both sides:
45x = 200.
Dividing both sides by 45:
x = 200/45.
Therefore, the original number is x = 40/9 or approximately 4.44 when rounded to two decimal places.
No.
GPT 3.5
Apologies for the earlier incorrect response. Let's try again to find the correct answer.
1. Multiply the original number by 2 1/2: This is equivalent to multiplying it by 5/2, so we have (x * 5/2).
2. Divide the previous result by 1 1/5: This is the same as dividing by 6/5, so now we have [(x * 5/2) ÷ (6/5)].
3. Subtract 7/18: [(x * 5/2) ÷ (6/5)] - 7/18 = 1 5/6 (or 16/6).
To eliminate fractions, we can convert the whole number and mixed number into improper fractions:
1 5/6 = (6 * 1 + 5) / 6 = 11/6.
Now our equation becomes:
[(x * 5/2) ÷ (6/5)] - 7/18 = 11/6.
Next, we simplify the expression:
(5x/2) ÷ (6/5) - 7/18 = 11/6.
To divide by a fraction, we can multiply by its reciprocal:
(5x/2) * (5/6) - 7/18 = 11/6.
Simplifying further:
(25x/12) - 7/18 = 11/6.
To eliminate the fractions, we can find the least common denominator, which is 36, and multiply both sides of the equation by it:
36 * [(25x/12) - 7/18] = 36 * (11/6).
Simplifying further:
(25x/12) * 36 - 7/18 * 36 = 11/6 * 36.
This gives us:
(6 * 25x) - (2 * 7) = 66.
Simplifying further:
150x - 14 = 66.
Adding 14 to both sides:
150x = 80.
Dividing both sides by 150:
x = 8/15.
Therefore, the original number is x = 8/15 or approximately 0.533 when rounded to three decimal places.
1. Multiply the original number by 2 1/2: This is equivalent to multiplying it by 5/2, so we have (x * 5/2).
2. Divide the previous result by 1 1/5: This is the same as dividing by 6/5, so now we have [(x * 5/2) ÷ (6/5)].
3. Subtract 7/18: [(x * 5/2) ÷ (6/5)] - 7/18 = 1 5/6 (or 16/6).
To eliminate fractions, we can convert the whole number and mixed number into improper fractions:
1 5/6 = (6 * 1 + 5) / 6 = 11/6.
Now our equation becomes:
[(x * 5/2) ÷ (6/5)] - 7/18 = 11/6.
Next, we simplify the expression:
(5x/2) ÷ (6/5) - 7/18 = 11/6.
To divide by a fraction, we can multiply by its reciprocal:
(5x/2) * (5/6) - 7/18 = 11/6.
Simplifying further:
(25x/12) - 7/18 = 11/6.
To eliminate the fractions, we can find the least common denominator, which is 36, and multiply both sides of the equation by it:
36 * [(25x/12) - 7/18] = 36 * (11/6).
Simplifying further:
(25x/12) * 36 - 7/18 * 36 = 11/6 * 36.
This gives us:
(6 * 25x) - (2 * 7) = 66.
Simplifying further:
150x - 14 = 66.
Adding 14 to both sides:
150x = 80.
Dividing both sides by 150:
x = 8/15.
Therefore, the original number is x = 8/15 or approximately 0.533 when rounded to three decimal places.