A man uses 1/8 of his salary after tax on house rent, and a 3/5 on transport, food and other household items. He then reserves 5/8 of the remainder on leisure and incidentals while saving the rest. if he saves$37135 every month. How much is his salary after tax.( round to the nearest whole number)​

let x be his salary after tax

house rent=1/8x

transport, food,=3/5x

total expenses, =1/8x + 3/5x

                          =29/40x

remainder amount =(x - 29/40x) = (1 - 29/40)x

leisure and incidentals,=5/8(1 - 29/40)x

amount saved = $37135

hence, the equation for his salary after tax is;

x = (29/40x) + 5/8(1 - 29/40)x + 37135

x = (29/40x) + (5/8x) - (29/64x) + 37135

x = (287/320x) + 37135

x - 287/320x = 37135

    33/320x = 37135

                x = 360096.97

to the nearest whole number, his salary after tax is $360097

Step-by-step explanation:

first represent his salary after tax by a variable

add the two expenses to get the total amount spent

substract the total amount spent from the variable to get the remainder

now fine 5/8 0f the remainder to get the amount spent on leisure and incidentals.

note that there was am amount that he saved.

base on this, we can now express an equation in terms of "

x" to calculate for his salary after tax  

answer;

the correct answer

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(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47