In a mixture of concrete, there are four
lb of cement mix for each pound of gravel. If the mixture contains a total of 215
lb of these two ingredients, how many pounds of gravel are there?
Well, because there are 4 lb of cement for 1 lb of gravel, the ratio would be 4:1 for cement and gravel, respectively. Each of the items added together would be 5 pounds, but 1 of each 5 pounds is gravel, so 1/5 of the mixture is gravel. 1/5 * 215 = 43
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the number of pounds of cement mix is represented by c, and the number of pounds of gravel is represented by g.
Given that there are four pounds of cement mix for each pound of gravel, we can write the equation:
c = 4g (equation 1)
We are also given that the total weight of the mixture is 215 pounds, so we can write another equation:
c + g = 215 (equation 2)
Now, we can use these two equations to solve for the number of pounds of gravel (g).
First, substitute equation 1 into equation 2:
4g + g = 215
Combine like terms:
5g = 215
Divide both sides by 5:
g = 215/5
g = 43
Therefore, there are 43 pounds of gravel in the mixture.