Concert two parts

Matej and Tom enjoyed the concert of their favourite musical group from the beginning until the end. After its first part, a ten-minute intermission followed. The second part of the concert was 40% shorter than its first part. The musicians performed live for a total of 120 minutes.
Decide for each of the following statements whether it is true, or not.
a) The first part of the concert was exactly half an hour longer than the second part of the concert. YES/NO
b) The first part of the concert lasted less than an hour. YES/NO
c) The second part of the concert lasted exactly three-quarters of an hour. YES/NO
(Write the solution procedure of the individual statements a), b), c).)

Result

a=

Yes

No

b=

Yes

No

c=

Yes

No

Step-by-step explanation:

$$\begin{gathered} q=100\%-40\%=1-\frac{40}{100}=0.6 \\ x+0+q\cdot x=120 \\ x+0+0.6\cdot x=120 \\ 1.6x=120 \\ x=\frac{120}{1.6}=75 \\ x=75 \\ y=q\cdot x=0.6\cdot 75=45\text{min} \\ X=x\to \text{h}=x:60\text{h}=75:60\text{h}=1.25\text{h} \\ Y=y\to \text{h}=y:60\text{h}=45:60\text{h}=0.75\text{h} \\ A=X-Y=1.25-0.75=\frac{1}{2}=0.5\text{h} \\ A=1/2\text{h} \\ a=1 \end{gathered}$$

$$\begin{gathered} X>1\text{h} \\ b=0 \end{gathered}$$

$$\begin{gathered} Y=3/4\text{h} \\ c=1 \end{gathered}$$

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