Problem 4 - Shopping spree
Problem 4 is all about working out how much money has been spent on a family shopping trip.
Maths teacher Chris Smith and pupils from Grange Academy are here to explain.
The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.
So here's the challenge:
All eleven members of the McTavish family have gone on a shopping trip to Killiemuir.
Ten of them spent exactly 拢20 each but Tam was extravagant. He spent 拢10 more than the average for the whole family.
How much did Tam spend?
Need a hint?
- Remember Tam spent 拢10 more than the average 鈥 not 拢10 more than everyone else.
- It might help to work out a formula to find the total money the family spent.
- You could try trial and improvement to get to the right answer.
Solution
Worked out the answer? Here's how you can do it.
Here is what we know:
- \(11\) people went on the shopping trip.
- \(10\) people spend \(拢20\) each.
- Tam spent \(拢10\) more than the average for the whole family.
We can use algebra to work out the answer
Step one
If we say Tam spent \(x\), we can work out an expression that shows the total that was spent.
\(\text{total} = 10 \times 20 + x\)
\( = 200 + x\)
Step two
We know that Tam spent \(拢10\) more than the average for the whole family. We can write this as:
\(x = 10 + \text{average}\)
Step three
If the total spend was \(拢200 + x\), then the average is \(\frac{1}{11}\) of this, as there were \(11\) people on the trip.
\(\text{average} = \frac{1}{11} (200 + x)\)
We can put this into our equation.
\(x = 10 + \frac{1}{11} (200 + x)\)
Step four
Simplify the equation by multiplying both sides by \(11\).
\(11x = 110 + 200 + x\)
Step five
Take \(x\) from each side.
\(10x = 110 +200\)
\( = 310\)
Step six
Divide both sides by \(10\)
\(x = 31\)
So we have worked out that Tam spent 拢31.
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