1. What is the value of X in a triangle that has 110° and 30°: 70°, 80°, 90°?
2. A map scale is 1cm to 20km. What is the real distance between two places which are 0.5 apart on the map?
3. When a jeweller sold a ring for €150, he made a profit of 50%. How much did the ring cost him at first?
4. A map has a scale of 1cm to 10km. What length of line on the map would represent a real distance of 40km?
5. Carpet is €6 per metre squared. If it cost €72 to cover a floor which is 3m wide, what is the length of the floor?
What are your answers?
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1. To find the value of X in a triangle with angles 110°, 30°, and X, we can use the property that the sum of the angles in a triangle is always equal to 180°. Therefore, we can calculate X by subtracting the sum of the other two angles from 180°. In this case, X = 180° - (110° + 30°) = 40°.
2. To determine the real distance between two places using a map scale, we can use the ratio between the map distance and the real distance. In this case, the map scale is 1cm to 20km. So, for every 1cm on the map, the real distance is 20km. To find the real distance between two places that are 0.5cm apart on the map, we can multiply 0.5cm by the ratio 20km/1cm. This gives us a real distance of 10km.
3. If the jeweler made a profit of 50% and sold the ring for €150, we can calculate the original cost of the ring by dividing the selling price by the percentage in decimal form plus 1. In this case, the percentage is 50%, or 0.50 in decimal form. Therefore, the original cost of the ring is €150 / (0.50 + 1) = €100.
4. The scale of 1cm to 10km means that for every 1cm on the map, the real distance is 10km. To find the length of a line on the map that represents a real distance of 40km, we can multiply the real distance by the ratio 1cm/10km. Therefore, the length of the line on the map would be 40km × (1cm/10km) = 4cm.
5. The cost of the carpet is €6 per square meter. To find the area of the floor, we need to multiply the width of the floor by its length. In this case, the width of the floor is 3m. To find the length of the floor, we can divide the total cost to cover the floor by the cost per square meter of the carpet. Therefore, the length of the floor is €72 ÷ (€6/m²) = 12m.