Answer:
the larger number is 50
Step-by-step explanation:
Notice there are two unknown numbers. Let's address the smaller one as x and the larger one as y. now we can write two equations from translating the phrases given into algebraic expressions:
"the sum of two numbers is 80" can be written as:
[tex]x+y=80[/tex]
Now the second phrase:
"The ratio of those two numbers is 3/5"
Notice here that in our ratio we need to use our small number (x) in the numerator of the quotient, and the larger number (y) in the denominator to make it in agreement with the small and larger numbers of the ratio [tex]\frac{3}{5}[/tex], and solve for x:
[tex]\frac{x}{y} = \frac{3}{5} \\x= \frac{3}{5}y[/tex]
Replace the value of x we just obtained in the first equation we wrote, so we obtain one equation with only one unknown hat we should be able to solve:
[tex]x+y=80\\\frac{3}{5} y+y=80\\\frac{3}{5} y+\frac{5}{5} y=80\\\frac{8}{5}y=80 \\8y=80*5\\8y=400\\y=\frac{400}{8} \\y=50[/tex]
Therefore the larger number (y) equals 50.
