Difficulty: Tricky
Rita is making lamingtons for her birthday party and cuts them precisely into 5-centimetre cubes. While playing around with an antique balance scale, she discovers that one lamington is equal to 50 grams plus half a lamington.
At her party, she eats one and a half lamingtons. How much did Rita’s dessert weigh?
Need a hint?
Remember two halves make a whole! Can you use this information to work out how much half a lamington weighs?
P.S. the fact that the lamingtons are 5-centimetre cubes is extra information you don’t need to solve the problem. Focus on the clue about its weight.
Brainteaser answer
Rita’s dessert of a lamington and a half weighs 150 grams in total.
Our main clue is that 1 lamington is equal to 50 grams plus half a lamington. Remember that two halves make a whole. So, 1 lamington is also equal to half a lamington plus half a lamington. We can write both equations like this:
1 lamington = 50 grams + half a lamington
1 lamington = half a lamington + half a lamington
For both equations to be true, half a lamington must equal 50 grams! So, a whole lamington weighs twice that at 100 grams. Now we can calculate Rita’s dessert of a lamington and a half, which equals 100 grams plus 50 grams, 150 grams in total.
We can also solve this problem using algebra. First, we define x as the mystery weight of a whole lamington. Then we write out the first clue about the lamington’s weight – one lamington is equal to 50 grams plus half a lamington – as an equation:
x = 50 + ½x, now we need to combine the x’s, so we subtract ½x from both sides of our equation:
½ x = 50, the weight of half a lamington! To find x on its own, we multiply both sides by 2:
x = 100, we’ve found the weight of a whole lamington!
Rita ate 1+ ½ lamingtons, which equals 100 + 50 grams, a total of 150 grams.