A contractor requires a cement mix that is 70% sand and 30% cement.
He has 700 kg of a cement mix that is 80% sand and 20% cement.
How much cement should he add so that he gets the required mix?
My set up:
required mix = (S)(.7) + (C)(3)
700kg = (S)(.8) + (C+X)(.2)
Is this even correct?
Your setup is not correct. Let's break down the solution step by step:
Let's assume "x" represents the amount of cement that the contractor needs to add.
1. Calculate the amount of sand in the required mix:
The contractor needs a cement mix that is 70% sand, so the amount of sand can be calculated as 0.7 times the total weight of the mix. Therefore, the amount of sand can be represented as 0.7 times (700 kg + x).
2. Calculate the amount of cement in the required mix:
The contractor needs a cement mix that is 30% cement, so the amount of cement can be calculated as 0.3 times the total weight of the mix. Therefore, the amount of cement can be represented as 0.3 times (700 kg + x).
3. Set up an equation:
The sum of the sand and cement amounts in the required mix should equal the amount of the initial mix. So we have the equation:
Amount of sand in required mix + Amount of cement in required mix = Amount of initial mix
0.7(700 + x) + 0.3(700 + x) = 700
Simplifying the equation:
0.7(700 + x) + 0.3(700 + x) = 700
490 + 0.7x + 210 + 0.3x = 700
700 + x = 700
1x = 700 - 490
1x = 210
Therefore, the contractor needs to add 210 kg of cement in order to get the required mix.
Your setup is almost correct, but there is a small mistake. The required mix should be (S)(0.7) + (C)(0.3), not (C)(3). The correct setup would be:
required mix = (S)(0.7) + (C)(0.3)
700 kg = (S)(0.8) + (C+X)(0.2)
Now, let's solve the problem using this correct setup. Let's break it down step by step:
Step 1: Convert the percentages to decimals.
The required mix is 70% sand and 30% cement, which in decimal form is 0.7 and 0.3, respectively.
The given cement mix is 80% sand and 20% cement, which in decimal form is 0.8 and 0.2, respectively.
Step 2: Express the quantities in terms of weight.
Let's assume the amount of cement to be added is X kg.
So, the amount of sand in the required mix would be 0.7(700) kg, and the amount of cement would be 0.3(700) kg.
The amount of sand in the given cement mix would be 0.8(700) kg and the amount of cement would be 0.2(700) kg.
Step 3: Set up the equation by balancing the amounts of sand and cement.
0.7(700) + 0.3(700) = 0.8(700) + 0.2(700 + X)
Step 4: Solve for X.
Multiply and simplify both sides of the equation:
490 + 210 = 560 + 0.2X + 140
Combine like terms:
700 = 700 + 0.2X + 140
Subtract 700 from both sides:
0.2X + 140 = 0
Subtract 140 from both sides:
0.2X = -140
Divide both sides by 0.2:
X = -140 / 0.2
X = -700
Since it doesn't make sense to have a negative amount of cement, there seems to be an error in the given information or the calculation. Please double-check the numbers or the requirements provided.
C / (S+c) = 0.3.
C = 0.8 * 700kg = 560kg.
C / (560+C) = 0.3,
C = 168 + .3C,
C - 0.3C = 168,
0.7C = 168,
C = 240kg.