Problems in steps

In your book, Maths Mela (Chapter 4, We the Travellers — II), many problems need more than one step. A good habit is to estimate first and then work out the exact answer. The members of a school council have raised ₹70,500. They want a Maths Lab worth ₹39,785, library books worth ₹9,545 and sports equipment worth ₹19,548. Is there enough money? Estimate: about ₹40,000 + ₹10,000 + ₹20,000 = ₹70,000. That is close to ₹70,500, so we must check exactly: ₹39,785 + ₹9,545 = ₹49,330, and ₹49,330 + ₹19,548 = ₹68,878. That is less than ₹70,500, so there is enough, with ₹1,622 left over.

A truck can carry 8,250 kg. A factory loads 3,675 kg of cement and 2,850 kg of steel. First add: 3,675 + 2,850 = 6,525 kg is loaded. Then subtract: 8,250 − 6,525 = 1,725 kg more can go on the truck.

At the Math Metric Mela, every student was to get a certificate. In Chittoor, 18,225 certificates were printed and 18,104 students came: 18,225 − 18,104 = 121 certificates were extra. In Jaunpur, 19,043 were printed but 19,265 students came, so there were too few: 19,265 − 19,043 = 222 certificates were short. In Raigad, 20,863 were printed and 19,974 students came: 889 were extra.

Priyanka Mohite is the first Indian woman to climb five Himalayan peaks above 8,000 metres. The book's table lists peaks she climbed. The highest is Mount Everest, 8,848 m, and the lowest is Mount Elbrus, 5,642 m. The difference is 8,848 − 5,642 = 3,206 m. Mount Kanchenjunga is 8,586 m, which is 8,586 − 5,642 = 2,944 m higher than Elbrus.

Mary sets out from Kolkata with ₹12,540. On the way her uncle gives her a gift of ₹4,900, so she has 12,540 + 4,900 = ₹17,440. She spends ₹3,275, leaving 17,440 − 3,275 = ₹14,165. Her ticket costs ₹2,645: 14,165 − 2,645 = ₹11,520. Souvenirs cost ₹1,275: 11,520 − 1,275 = ₹10,245. So Mary has ₹10,245 left. In a problem like this, every number has to be used, and the gift is money she gains, not money she spends.

Sometimes we choose numbers to get close to a target. Which two of 5,205, 6,220, 7,095, 8,455 and 4,840 have a sum closest to 10,000? The two smallest, 5,205 + 4,840 = 10,045, are just 45 away. Every other pair adds up to more than 11,000.