# Solve for y (3y+14)/4+(y+29)/5=15

3y+144+y+295=15
Factor the equation.
To write 3y+144 as a fraction with a common denominator, multiply by 55.
3y+144⋅55+y+295=15
To write y+295 as a fraction with a common denominator, multiply by 44.
3y+144⋅55+y+295⋅44=15
Write each expression with a common denominator of 20, by multiplying each by an appropriate factor of 1.
Multiply 3y+144 and 55.
(3y+14)⋅54⋅5+y+295⋅44=15
Multiply 4 by 5.
(3y+14)⋅520+y+295⋅44=15
Multiply y+295 and 44.
(3y+14)⋅520+(y+29)⋅45⋅4=15
Multiply 5 by 4.
(3y+14)⋅520+(y+29)⋅420=15
(3y+14)⋅520+(y+29)⋅420=15
Combine the numerators over the common denominator.
(3y+14)⋅5+(y+29)⋅420=15
Rewrite (3y+14)⋅5+(y+29)⋅420 in a factored form.
Apply the distributive property.
3y⋅5+14⋅5+(y+29)⋅420=15
Multiply 5 by 3.
15y+14⋅5+(y+29)⋅420=15
Multiply 14 by 5.
15y+70+(y+29)⋅420=15
Apply the distributive property.
15y+70+y⋅4+29⋅420=15
Move 4 to the left of y.
15y+70+4⋅y+29⋅420=15
Multiply 29 by 4.
15y+70+4y+11620=15
19y+70+11620=15
19y+18620=15
19y+18620=15
19y+18620=15
Solve the equation.
Multiply both sides of the equation by 20.
19y+186=15⋅(20)
Remove parentheses.
19y+186=15⋅(20)
Multiply 15 by 20.
19y+186=300
Move all terms not containing y to the right side of the equation.
Subtract 186 from both sides of the equation.
19y=300-186
Subtract 186 from 300.
19y=114
19y=114
Divide each term by 19 and simplify.
Divide each term in 19y=114 by 19.
19y19=11419
Cancel the common factor of 19.
Cancel the common factor.
19y19=11419
Divide y by 1.
y=11419
y=11419
Divide 114 by 19.
y=6
y=6
y=6
Solve for y (3y+14)/4+(y+29)/5=15

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