Answer: Victor should give 28 tools to Ilya.
Step-by-step explanation:
Since we have given that
Ratio of the number of Victor's tools to the number of IIya's tools = 5:2
Let the number of Victor's tools be 5x
Let the number of Ilya's tools be 2x
According to question, Victo has 42 more tools than Ilya.
So, our equation becomes,
[tex]5x-2x=42\\\\3x=42\\\\x=\dfrac{42}{3}=14[/tex]
So, number of tools Victor has 5x=5×14=70
Number of tools Ilya has 2x = 2× 14 =28
Let the number of tools that Victor should give to Ilya be 'y' so that the ratio of the number of victor's tools to the number of Ilya's tools is 3:4.
According to question, it becomes,
[tex]\dfrac{70-y}{28+y}=\dfrac{3}{4}\\\\4(70-y)=3(28+y)\\\\280-4y=84+3y\\\\280-84=3y+4y\\\\196=7y\\\\y=28[/tex]
Hence, Victor should give 28 tools to Ilya.
