A ratio equals 5 : 8. If the antecedent (first term) is 40, what is the consequent (second term)?

Introduction / Context:
Scaling a ratio to actual numbers requires multiplying both terms by the same factor. If the first term becomes 40, compute the common multiplier and apply it to the second term to find the consequent.

Given Data / Assumptions:

• Ratio = 5 : 8
• Antecedent (first term) after scaling = 40

Concept / Approach:
Find k such that 5k = 40 ⇒ k = 8. Then consequent = 8k = 8 * 8 = 64.

Step-by-Step Solution:
5k = 40 ⇒ k = 8Consequent = 8k = 8 * 8 = 64

Verification / Alternative check:
40 : 64 simplifies by 8 to 5 : 8, agreeing with the original ratio.

Why Other Options Are Wrong:
25 and 48 are inconsistent with 5k = 40; “None” is unnecessary since 64 is correct; 56 corresponds to k = 7, not matching 40.

Common Pitfalls:
Adding 3 to get 8 from 5 and then doing the same for 40 (incorrect reasoning). Ratios scale multiplicatively, not additively.

Final Answer:
64