the ratio of horseshoes to shamrock was 11 to 2, and five times the number of shamrocks was 3 less than the number of horseshoes. how many were shamrocks?

Answer 1

first, represent the unknowns with variables:
let x = number of shamrocks
let y = number of horseshoes
then set up equations according to the conditions given:
(1) y/x = 11/2
(2) 5x = y - 3
there are several ways to solve this,, if we choose to solve it by substitution method,,
choose an equation (in this case, equation (1)), then express one of the variables in terms of the other variable,, thus if we express y in terms of x:
y/x = 11/2
y = (11x)/2
now, you substitute this to equation (2):
5x = y - 3
5x = (11x)/2 - 3

then solve for x to get number of shamrocks.

hope this helps~ :)