Clearance - vacation

The Sobotka family checked their suitcases before leaving on holiday. Their four suitcases had weights in the ratio 3:4:5:8. The total weight of all four suitcases was 60 kg. The maximum allowed weight per 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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