Solving Tricky 11+ Maths Questions: A Step-by-Step Guide

Hi everyone, in this article we look at Solving Tricky 11+ Maths Questions! Today, we’re going to be looking at a maths question that a lot of children found quite tricky. But don’t worry, we’ll go through it step-by-step and see what the optimal way of solving it could be. There are actually different ways to approach this problem, but we’re going to focus on a logical method that will help you understand the process you need to go through.

Solving Tricky 11+ Maths Questions: The Question

So, here’s the question:

Joanne, Sarah, and Chang had 60 beads each. Joanne gave two-fifths of her beads to Chang. Sarah gave some of her beads to Chang. Chang had three times the total of the remaining beads. How many beads did Sarah give Chang?

Breaking It Down

Solving tricky 11+ maths questions can be a challenge, so let’s start by breaking down the information we’ve been given:

• Joanne, Sarah, and Chang each had 60 beads to begin with
• Joanne gave two-fifths of her beads to Chang
• Sarah gave an unknown number of her beads to Chang
• Chang ended up with three times the total of the remaining beads

Solving the Problem

Step 1: Calculate the Total Number of Beads

First, we need to work out the total number of beads that Joanne, Sarah, and Chang had altogether. We know they each had 60 beads, so:

60 × 3 = 180

Therefore, the three of them had a total of 180 beads.

Step 2: Calculate How Many Beads Joanne Gave to Chang

Next, we need to figure out how many beads Joanne gave to Chang. We know she gave two-fifths of her beads away. To calculate two-fifths of 60:

60 ÷ 5 = 12 × 2 = 24

So, Joanne gave 24 beads to Chang, and she had 36 left for herself.

Step 3: Determine the Distribution of Beads

Now, we know that Chang ended up with three times the total of the remaining beads. This means that Joanne and Sarah must have had one-quarter of the beads between them, and Chang had three-quarters.

To calculate one-quarter of the total beads:

180 ÷ 4 = 45

Therefore, Joanne and Sarah had 45 beads left between them, and Chang must have had the rest:

180 - 45 = 135

We can double-check this by confirming that 45 multiplied by 3 equals 135.

Step 4: Calculate How Many Beads Sarah Gave to Chang

Finally, we can work out how many beads Sarah gave to Chang. We know that Chang had 135 beads in total, and 60 of those were his own to begin with. Joanne gave him 24, so:

135 - 60 - 24 = 51

Therefore, Sarah must have given Chang 51 beads.

Checking Our Answer

Let’s just run through everything one more time to make sure our answer makes sense:

• Joanne, Sarah, and Chang started with 60 beads each
• Joanne gave 24 beads to Chang, leaving her with 36
• Chang now had 84 beads (his original 60 plus the 24 from Joanne)
• We know Chang ended up with 135 beads
• So, 135 – 84 = 51, which is the number of beads Sarah must have given him
• This leaves Sarah with 9 beads (her original 60 minus the 51 she gave away)

Conclusion

So, to answer the question: Sarah gave Chang 51 beads, and she had 9 left for herself.

I know we’ve taken a bit longer going through the explanation here, but that’s just to ensure understanding. In an actual exam, you wouldn’t spend this much time on a single question. The process will be much quicker once you’re familiar with it.

The key things to remember are:

1. Read the question carefully and note down the important information
2. Break the problem down into steps
3. Double-check your answer at the end to make sure it makes sense

I hope this has helped make the process a lot clearer, and that you feel more confident tackling similar questions in the future. Remember, practice makes perfect!

If you have any other questions, just ask in our Telegram Group and we’ll be happy to help. Until next time, take care everyone!

So we leave you with one last question. Have we helped you in Solving Tricky 11+ Maths Questions?

Need more support? Purchase one of our Problem-Solving Courses to further develop your child’s problem solving skills.