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?
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~ :)
To solve this problem, let's assume the number of horseshoes is represented by "x" and the number of shamrocks is represented by "y."
Based on the given information, we have two equations:
1) Ratio of horseshoes to shamrocks = 11:2
This can be written as: x/y = 11/2
2) Five times the number of shamrocks was 3 less than the number of horseshoes.
This can be expressed as: 5y = x - 3
Now we'll solve this system of equations using substitution:
From equation (1), we can express x in terms of y:
x = (11/2) * y
Substituting this value of x into equation (2):
5y = (11/2) * y - 3
To eliminate the fraction, we can multiply everything by 2:
10y = 11y - 6
Rearranging the equation:
11y - 10y = 6
y = 6
Therefore, the number of shamrocks is 6.
To find out how many shamrocks there were, we can use algebra to solve the problem.
Let's represent the number of horseshoes as 'x', and the number of shamrocks as 'y'.
According to the problem, the ratio of horseshoes to shamrocks is 11 to 2, so we can write the equation as:
x/y = 11/2
Additionally, the problem states that five times the number of shamrocks was 3 less than the number of horseshoes, which can be represented by the equation:
5y = x - 3
Now we have a system of equations that we can solve simultaneously. Let's start by solving the first equation for 'x':
x/y = 11/2
Multiply both sides by 'y' to isolate 'x':
x = (11/2)y
Substitute this value of 'x' into the second equation:
5y = (11/2)y - 3
Multiply both sides by 2 to get rid of the fraction:
10y = 11y - 6
Subtract 11y from both sides:
-1y = -6
Divide both sides by -1:
y = 6
Therefore, there were 6 shamrocks.