One number is six more than a second number. four times the first is 10 less than 6 times the second. Find the numbers.
1 answer:
![\sf{\bold{\blue{\underline{\underline{Given}}}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cbold%7B%5Cblue%7B%5Cunderline%7B%5Cunderline%7BGiven%7D%7D%7D%7D%7D)
- One number is six more than a second number.
- four times the first is 10 less than 6 times the second.⠀⠀⠀⠀
![\sf{\bold{\red{\underline{\underline{To\:Find}}}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cbold%7B%5Cred%7B%5Cunderline%7B%5Cunderline%7BTo%5C%3AFind%7D%7D%7D%7D%7D)
![\sf{\bold{\purple{\underline{\underline{Solution}}}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cbold%7B%5Cpurple%7B%5Cunderline%7B%5Cunderline%7BSolution%7D%7D%7D%7D%7D)
⠀⠀⠀⠀
In questions given,One number is six more than a second number.
if second number is a
first number is a+6.
and,
four times the first is 10 less than 6 times the second.
So,
4×(a+6)=6a-10
we have to solve this.
we,get our second number =a=17.
So,
first number =a+6=17+6=23
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See Below.
Step-by-step explanation:
We are given that:
![\angle ABC \cong \angle DEC\text{ and } \angle GFE \cong \angle DCE](https://tex.z-dn.net/?f=%5Cangle%20ABC%20%5Ccong%20%5Cangle%20DEC%5Ctext%7B%20and%20%7D%20%5Cangle%20GFE%20%5Ccong%20%5Cangle%20DCE)
By vertical angles:
![\displaystyle \angle DEC\cong \angle GEF\text{ and } \angle DCE\cong \angle ACB](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cangle%20DEC%5Ccong%20%5Cangle%20GEF%5Ctext%7B%20and%20%7D%20%5Cangle%20DCE%5Ccong%20%5Cangle%20ACB)
Hence, by substitution:
![\displaystyle \angle ABC\cong \angle GEF\text{ and } \angle GFE\cong \angle ACB](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cangle%20ABC%5Ccong%20%5Cangle%20GEF%5Ctext%7B%20and%20%7D%20%5Cangle%20GFE%5Ccong%20%5Cangle%20ACB)
Then by Angle-Angle Similarity:
![\Delta ABC \sim \Delta GEF](https://tex.z-dn.net/?f=%5CDelta%20ABC%20%5Csim%20%5CDelta%20GEF)