### Video Transcript

Welcome to puzzle time. Here’s puzzle number one. This puzzle concerns a bow and arrow salesman with a slightly mismatching
jumper and a pair of trousers. Here he is now, jumping up and down saying get your bow and arrow
here. Twenty one dollars for the pair! But when his first customer comes along, he says but what if I just want an
arrow. How much? Now the bow and arrow salesman doesn’t wanna make it too easy for the
customer to just buy an arrow, so they say, “Well the bow is twenty dollars more than the arrow.”

And at this point in the animation, they realised that the bow and arrow
salesman hasn’t been jumping up and down as we might have thought at first, but he’s just been
floating in the air all the time. But that was soon fixed by the animator. And at that point, the customer neatly sums up the question by saying the bow
and arrow are twenty one dollars for the pair. The bow is twenty dollars more than the arrow,
how much is the arrow? Okay, you’ve got three seconds to think about it. Maybe you wanna pause the
video while you work this out.

Well hopefully, you’ve got an answer for that now, but let’s do a little bit of
algebra and see how we can work it out. So let’s define our variables. Let 𝑎 be the
cost of the arrow and let 𝑏 be the cost of the bow. And let’s make sure we know what unit we’re specifying those variables to be
and it’s dollars in this case. So we know that the arrow plus the bow cost twenty one dollars
together, so 𝑎 plus 𝑏 is equal to twenty one.

And we also know that the bow cost twenty dollars more than the arrows, so the
𝑏 is the price of the arrow plus twenty. And what we’ve created is two simultaneous equations. We’ve got equation number
one and we’ve got equation number two. Now in equation number two, we can see that the value
𝑏 is equal to 𝑎 plus twenty. So we can replace the 𝑏 in equation one with 𝑎 plus twenty like this. And now we’ve got an equation with just one thing that we don’t know, so
we can do a bit of simplifying and rearranging and we can solve this.

Well without any modification going on, the brackets are fairly irrelevant, so
we can ignore those for now. And we’ve got 𝑎 plus 𝑎 which is
two 𝑎 and then another twenty on the left-hand side and we’ve got twenty-one on
the right-hand side. Now if I subtract twenty from both sides of my equation then twenty minus twenty is nothing on the left-hand side, so I’m just left
with two 𝑎. And on the right-hand side, twenty-one take away twenty is just one. So I know that two 𝑎 is equal to one. Well I want to know what
one 𝑎 is, the cost of one arrow. So if I divide both sides by two, I get an answer of two 𝑎 divided by two is just 𝑎
and one divided by two is a half or nought point five.

Now remember that 𝑎 was in dollars, so that’s nought point five
dollars, but we don’t just leave that as one decimal place. If we’re dealing with money, we’re
gonna keep that in to two decimal places or we could just say 𝑎 is fifty cents. So
the price of an arrow is nought point five dollars or fifty cents. And although the question didn’t ask for it, we can work out the price of a
bow. So that’s 𝑎 nought point five plus twenty. So that’s twenty point five. And again, being money, we’ve got to have two decimal places. So the bow is twenty dollars and fifty cents. Hope you worked it out and hope you
found our explanation useful.