6. Give a Teacher's Solution using algebra for the followingproblem: A truck contains 1000 pounds of sand and concrete in the ratio 2 : 3. After x pounds of sand is added, the ratio of the sand and concrete becomes 4:5. Find x

Answer:   80 poundsStep-by-step explanation:The problem can be worked in two parts. For the first part, we will find the amounts of sand and concrete in the truck. Then, we will use those numbers in the second part to find the added sand.The given relations are ...   s + c = 1000 . . . . . . . . there are 1000 pounds total of sand and concrete   s/c = 2/3 . . . . . . . . . . . the ratio of sand to concrete is 2:3Multiplying the second equation by c, we get an expression we can substitute into the first equation.   s = (2/3)c   (2/3)c + c = 1000 . . . . . . substitute for s   5/3c = 1000 . . . . . . . . . . collect terms   c = 1000(3/5) = 600 . . . multiply by the inverse of the coefficient of c   s = 2/3(600) = 400 . . . . find s using the relation aboveNow, we know the truck initially contains 400 pounds of sand and 600 pounds of concrete.__When we add x pounds of sand, the ratio of the mix changes to 4/5:   (s+x)/c = (400 +x)/600 = 4/5   400 +x = (4/5)(600) = 480 . . . . . . multiply by 600   x = 80 . . . . . . . . . . . . . . . . . . . . . . . subtract 400The amount of added sand is x = 80 pounds.