Three quarters of a number added to two and a half of the number gives 13. Find the number

Analyze the question: We need a number x such that three quarters of x plus "two and a half" of x equals 13.

Interpretation 1: "two and a half of the number" means 2½ × x

(3/4)x + (5/2)x = 13 (3/4)x + (10/4)x = 13 (13/4)x = 13 x = 13 × 4/13 = 4

This works out neatly, and the 13 in the numerator cancels the 13 on the right. That is a good sign we have the intended reading.

Check: (3/4)(4) = 3 (5/2)(4) = 10 3 + 10 = 13 ✓

Checking the other options (for confidence):

• x = 5: 3.75 + 12.5 = 16.25 ✗
• x = 6: 4.5 + 15 = 19.5 ✗
• x = 7: 5.25 + 17.5 = 22.75 ✗

Tip: When the sum of fractions has the same number as the total (here 13/4 and 13), expect the answer to be a simple whole number. Always convert mixed numbers like 2½ to improper fractions (5/2) before computing, and verify by substituting your answer back.