# Mathematics Problem Solving With Solution

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Let's suppose that each of the four tractors ploughed $x$ hectares a day.

Therefore in 5 days they ploughed $5 \cdot 4 \cdot x = 20 \cdot x$ hectares, which equals the area of the whole field, 2880 hectares. Hence, each of the four tractors would plough 144 hectares a day.

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.

Problem 9The first year, two cows produced 8100 litres of milk.

The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year.

They decided to plant birches and roses at the school's backyard. If each girl planted 3 roses, there are $\frac$ girls in the class. Therefore $\frac 3(24 - x) = 24$ $x 9(24 - x) = 3\cdot 24$ $x 216 - 9x = 72$6 - 72 = 8x$$\frac = x$$x = 18$So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches. While each girl planted 3 roses, every three boys planted 1 birch. Problem 14 A car left town A towards town B driving at a speed of V = 32 km/hr. Let us consider only the trip from C to B, and let$x$be the number of hours the driver spent on this trip. b) By the time of the meeting at station C the freight train rode for$\frac \frac$hours, i.e. Therefore it left station B at - (1 \frac) = 10 \frac$ hours, i.e. So she increased her speed by 10 km/hr and she arrived at city B 36 minutes earlier than she planned. If she continued at the same speed she would be $minutes late, i.e. So, she covered the distance between A and B in \frac$ hr, and it was 36 min less than planned. When we equalize the expressions for the scheduled time, we get the equation: $\frac - \frac = 2 \frac \frac$ $\frac = \frac$ $\frac = \frac$ x - 50 = 4x 200x = 250$So, the distance between cities A and B is 250 km. the planned time on the road is$\frac - \frac\$ hr. Problem 12To deliver an order on time, a company has to make 25 parts a day.

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