A silo contains a mixture of lentils and corn. If 50 bushels of lentils were added to this mixture, there would be twice as many bushels of lentils as bushels of corn. If 150 bushels of corn were added to the original mixture, there would be the same amount of corn as lentils. How many bushels of each are in the silo?As the answer the book gets:There are 350 bushels of lentils and 200 bushels of corn in the silo.How do I get the equations though?tyyyyy
This is a simple question of VI grade. Stan, silly fighting doesn't make you wise. Better you apologize, or else this will be reported as abusive.
Missing a word in the first problem. Is it difference? y - x = 3 The first problem is just a matter of translating words into mathematical symbols. Call the smaller number x and the larger number y. twice 2 * the larger number y is = 36 more than 36 + three times 3 * the smaller number x 2*y = 36 + 3*x In the second problem, you also need to know the formulas for perimeter and area of a rectangle. Call the width x and the length y. 2x + 2y = 64 y = 14 + x Find x*y
Let L = # bushels of lentils (originally) C = # of bushes of corn originally Then L + 50 = # bushels of lentils if 50 bushels are added and C + 150 = # bushels of corn if 150 were added Then the given information translates into these equations: L + 50 = 2C C + 150 = L The easiest way now to solve the system of equations is probably to substitute C + 150 for L in the first equation: C + 150 + 50 = 2C or 200 = C Then, since C + 150 = L, we have 200 + 150 = L 350 = L (And we can see how people like Prasad get to be top contributors - just say here's the answer... to grab the first spot before he's figured out the answer. Really childish. And no, I never do that because I don't care about the glory.) And, teen b, I do not apologize to children for calling them children.
Let x = bushels of lentils Let y = bushels of corn Given: If 50 bushels of lentils were added to this mixture, there would be twice as many bushels of lentils as bushels of corn: -----> x + 50 = 2y (eq. #1) If 150 bushels of corn were added to the original mixture, there would be the same amount of corn as lentils: y + 150 = x (eq. #2) Rewrite the equations so that the variables are on the left side of the = sign, and the constant is on the right. eq. #1 x + 50 = 2y Subtract x from both sides 2y - x = 50 eq. #2 y + 150 = x Subtract y from both sides x - y = 150 Rewrite equations so that the x and y variables line up. eq. #1: - x + 2y = 50 x - y = 150 When you have a system of equations, the goal is to have one variable cancel out when the equations are added or subtracted. Sometimes, you have to multiply one of the equations by a number that will allow this to happen. However, in your problem (or system), the x variable will cancel out if you add eq. #1 to eq. #2. Add eq. #1 to eq. #2 (- x + 2y = 50) +( x - y = 150) ___________ -----> y = 200 I got y = 200 by adding the equations (see below) -x + x -----> x cancels out 2y + (-y) = y 50 + 150 = 200 This leaves you with : y = 200 Now substitute y = 200 into either equation and solve for x x - y = 150 x - (200) = 150 Add 200 to both sides x = 350 x = 350, y = 200 Check: When 50 is added to x, x = 2y 350 + 50 = 2(200) 400 = 400 When 150 is added to y, y = x 200 + 150 = 350 350 = 350 The answer checks out. x = 350 (lentils) y = 200 (corn) I hope that helps, good luck.
A good question.... Here is the answer : Let us assume that there are 'L' bushels of lentils and 'C' bushels of corn in the silo. According to the first statement, If 50 bushels of lentils were added to this mixture, there would be twice as many bushels of lentils as bushels of corn. L + 50 = 2 C.............That forms Equation (1) According to the second statement, If 150 bushels of corn were added to the original mixture, there would be the same amount of corn as lentils. C + 150 = L................That forms Equation (2) Equation (2) can be written as L = C +150 Put this value of L as C + 150 in equation (1) equation (1) becomes.... C + 150 + 50 = 2 C or....... C+200 = 2C So, C = 200 From Equation (2), we know that L = C + 150 Substitute the value of C as 200, L = 200 + 150 = 350 So, There are 350 bushels of lentils and 200 bushels of corn in the silo.
