The ratio of horseshoes to shamrocks was 11 to 5, and two times the number of shamrocks was 12 less than the number of horseshoes. How many were shamrocks?
thank you :)
Rachal, I messed that up.
H/S=11/5 so 5H=11S
and 2S+12=H
From the first equation H=11S/5
putting that into the second.
2S+12=11S/5
multiplying both sides by 5
10S+60=11S
adding sixty to both sides and subtracting 11S from both sides.
-S=-60 or S=60
so H=11*60/5=132
can someone make up 5 ratio road problems?
To solve this problem, let's assign variables to the number of horseshoes and shamrocks.
Let's say the number of horseshoes is represented by 'H' and the number of shamrocks is represented by 'S'.
According to the problem, the ratio of horseshoes to shamrocks is 11 to 5, which can be written as:
H/S = 11/5
We are also given that two times the number of shamrocks is 12 less than the number of horseshoes, which can be written as:
2S = H - 12
Now, we can solve the above equations simultaneously to find the values of H and S.
First, let's solve the equation H/S = 11/5 for H:
H = (11/5)S
Substitute this value of H in the second equation:
2S = (11/5)S - 12
Multiply through by 5 to get rid of the fractions:
10S = 11S - 60
Now, bring all the S terms to one side and the constant terms to the other side:
11S - 10S = 60
S = 60
Therefore, the number of shamrocks is 60.
I hope this helps! Let me know if you have any further questions.
To find the number of shamrocks, let's set up a system of equations based on the given information.
Let's assume the number of horseshoes is "h" and the number of shamrocks is "s".
The first piece of information states that the ratio of horseshoes to shamrocks is 11 to 5. This can be written as:
h/s = 11/5 (Equation 1)
The second piece of information states that twice the number of shamrocks is 12 less than the number of horseshoes. Mathematically, this can be represented as:
2s = h - 12 (Equation 2)
Now we have a system of equations. We can solve it to find the values of h and s.
Let's solve Equation 2 for "h" in terms of "s":
h = 2s + 12
Substitute this expression for "h" in Equation 1:
(2s + 12)/s = 11/5
Cross-multiply:
5(2s + 12) = 11s
Expand and simplify:
10s + 60 = 11s
Subtract 10s from both sides:
60 = 11s - 10s
60 = s
Therefore, there were 60 shamrocks.