Clearance - vacation

The Sobotkas checked their suitcases for clearance when they were leaving for their vacation. Their four suitcases had weights of 3 : 4 : 5 : 8. The total weight of all four suitcases was 60 kg. The maximum weight allowed for one piece of luggage is 25 kg.
a) Calculate the weight of the lightest suitcase in kg.
b) Decide whether all suitcases can be checked in.

Result

a =  9 kg
x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} m=60\text{kg} \\ a:b:c:d=3:4:5:8 \\ a=\frac{3}{3+4+5+8}\cdot m=\frac{3}{3+4+5+8}\cdot 60=9=9\text{kg} \\ b=\frac{4}{3+4+5+8}\cdot m=\frac{4}{3+4+5+8}\cdot 60=12\text{kg} \\ c=\frac{5}{3+4+5+8}\cdot m=\frac{5}{3+4+5+8}\cdot 60=15\text{kg} \\ d=\frac{8}{3+4+5+8}\cdot m=\frac{8}{3+4+5+8}\cdot 60=24\text{kg} \end{gathered}$$

$$\begin{gathered} a,b,c,d<25\text{kg} \\ x=1 \end{gathered}$$

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