Algebra
Anna's age is twice that of David's and half that of Bob's. The total of all their ages is 21. How old is Bob?
A box of biscuits
A box of biscuits contains 36 biscuits. 20 biscuits have foil wrappers. 15 are chocolate biscuits with foil wrappers. If 9 are not chocolate and do not have a foil wrapper, then how many chocolate biscuits are there?
First we need to set the variables:
ReplyDeleteLet Anne be 'a'. Let Bob be 'b'. Let David be 'd'.
Now we can create a formula:
a + b + d = 21.
Next we need to substitute the variables for one after calculating it. This may sound confusing but it will make sense:
a = 2d This is because the question states that Anne's age is twice that of David's.
b = 2a This is because the question also states Anna's age is half that of Bob's.
This then means that b = 4d when you substitute the a from the first equation into the second.
Now, remember that formula we created earlier? We can use that now by substituting the values that we've calculated:
2d + 4d + d = 21
7d = 21
d = 3
Now it may seem like we're done, but remember, the question asks for Bob's age. This means we substitute 4 * d into our new value of d and we get 4 * 3, which is 12. NOW, we're done