Solving Math Problems With Solutions

Solving Math Problems With Solutions-86
After 3 hours on the road the driver stopped for 15 min in town C. Then the distance from C to B is $S = 40\cdot x$ km.Because of a closed road he had to change his route, making the trip 28 km longer. Solution: From the statement of the problem we don't know if the 15 min stop in town C was planned or it was unexpected. If the driver could use the initial route, it would take him $x - \frac = x - \frac$ hours to drive from C to B.

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Problem 1 A salesman sold twice as much pears in the afternoon than in the morning. Then Mary and Lucy picked $2x$ and $x 2$, respectively.

If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon? This must be equal to 360.$3x = 360$$x = \frac$$x = 120$ Therefore, the salesman sold 120 kg in the morning and $2\cdot 120 = 240$ kg in the afternoon. Together the three of them picked 26 kg of chestnuts. So $x 2x x 2=26$$4x=24$$x=6$ Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.

How many litres were milked from each cow each year?

Solution: Let x be the amount of milk the first cow produced during the first year.

At the new production rate they made: $3\cdot 25 (x - 3)\cdot 30 = 75 30(x - 3)$ Therefore: $25 x = 75 30(x -3) - 100$ $25x = 75 30x -90 - 100$ $190 -75 = 30x -25$ $115 = 5x$ $x = 23$ So the company worked 23 days and they made $23\cdot 25 100 = 675$ pieces.

Problem 13 There are 24 students in a seventh grade class. Then the number of birches is - x$, and the number of boys is \times (24-x)$.So 00 \frac\cdot x \frac \cdot (8100 - x) = 9100$ Therefore 00 \fracx \frac(8100 - x) = 9100$$\fracx = 190$$x = 3800$Therefore, the cows produced 38 litres of milk the first year, and 70$ and 30$ litres of milk the second year, respectively.Problem 10The distance between stations A and B is 148 km.An express train left station A towards station B with the speed of 80 km/hr.At the same time, a freight train left station B towards station A with the speed of 36 km/hr. Solution a) Let x be the distance between stations B and C.Solution: Let $x$ be the number of days the company worked.Then 25x is the number of parts they planned to make.Solution: Let $x$ be the number of kilograms he sold in the morning. Problem 2 Mary, Peter, and Lucy were picking chestnuts. Solution: Let $x$ be the total number of pages in the book, then she finished $\frac\cdot x$ pages.Then she has $x-\frac\cdot x=\frac\cdot x$ pages left.Then the second cow produced $(8100 - x)$ litres of milk that year.The second year, each cow produced the same amount of milk as they did the first year plus the increase of \%$ or \%$.

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