Comment
Author: Admin | 2025-04-28
And the area of a parallelogram is base × height.A triangle whose base equals one side of the parallelogram, and whose height reaches the opposite side of the parallelogram, has exactly half the area of a parallelogram.This is true for a pair of triangles as well – if the pair of triangles span one side and if their heights reach the opposite side.To make solving this easier, you can start by labelling the unknown areas with letters a to f. And let the area of the red triangle be x.Presh Talwalkar from Mind You Decisions, breaks down the solution in his video here.Question 6 Answer (Part a)The key is to remember that Helen and Ivan have the same number of coins.Let’s look and compare the total number of coins for each type.Ivan has 40 more 20-cent coins than Helen. For them to have the same number of coins, you have to ‘balance’ this out in terms of the 50-cent coins.This means Helen must have 40 more of the 50-cent coins than Ivan.Let’s now compare the amount of money of each coin type that Helen has, minus that of Ivan.Since Helen has 40 fewer (104 – 64) of the 20-cent coins, so Helen will have:– 40 × 0.2 = – 8This means she has $8 less than Ivan (in 20-cent coins).On the other hand, Helen has 40 more of the 50-cent coins than Ivan. So she will have:+ 40 × 0.5 = 20This means she has $20 more than Ivan (in 50-cent coins).Now, you can add this together to find out how much more or less money Helen has.– 8 + 20 = 12Therefore, Helen has $12 more than Ivan.Question 6 Answer (Part b):The total mass of Helen’s coin is 1.134kg. And you know that a 50-cent coin is 2.7g heavier than a 20-cent coin.From the first part of the question, you can see that if you had Helen’s coins, you can ‘exchange’ 40 of the 50-cent coins for 40 of the 20-cent coins, that will be the total coins Ivan has. And you can get the weight difference from that.Let’s compare the weight of Helen’s coins to Ivan’s coins.In terms of the 20-cent coins, subtract 40 of the 20-cent coins, multiplied by the weight of the coins.– 40 × 0.2 weightIn terms of the 50-cent coins, add 40 of the 50-cent coins, multiplied by the weight.+40 × 0.5 weightSo the net impact of this, Helen compared to Ivan, has 40 more of the heavier coins – 40 more of the 50-cent coins, compared to the 20-cent coins than Ivan.+ 40 × 0.5 weight / 40 × (0.5 – 0.2 weight)You know the difference in weight between 50-cent and 20-cent coins is 2.7 grams. Therefore, you can substitute that in the equation.+ 40 × 0.5 weight / 40 × (2.7 g) –> 40 × (2.7 g) = 108gSo Helen’s weight of coins is 108 g more than Ivan.To get Ivan’s weight, we take Helen’s coins and subtract by 108g.1134g – 108g
Add Comment