Carla has \(\frac{1}{4}\) more sweaters than cardigans, and \(\frac{2}{5}\) fewer cardigans than turtle­ necks. If she has at least one of each item, what is the minimum total number of turtlenecks plus sweaters that Carla could have?

A. 10
B. 15
C. 20
D. 35
E. 45
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Don't know why this one felt hard, from the text you get:

(1) \(S = \frac{5C}{4}\)
(2) \(C = \frac{3T}{5} => T = \frac{5C}{3}\)

\(T+S = \frac{5C}{3} + \frac{5C}{4} = \frac{35C}{12}\)

Since C>0, minimum T+S is when C = 12: ans 35 (D).

Given:
1. Carla has \(\frac{1}{4}\) more sweaters than cardigans.
2. Carla has \(\frac{2}{5}\) fewer cardigans than turtle­ necks.
3. She has at least one of each item.

Asked: What is the minimum total number of turtlenecks plus sweaters that Carla could have?

Let number of sweaters, cardigans and turtle necks be s, c & t respectively

1. Carla has \(\frac{1}{4}\) more sweaters than cardigans.
s:c = 5:4

2. Carla has \(\frac{2}{5}\) fewer cardigans than turtle­ necks.
c:t = 3:5

s:c:t = 15:12:20

Minimum total number of turtlenecks plus sweaters that Carla could have = 15 + 20 = 35

IMO D
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