Primary 5 (11 yo) Math Question

Question

There are 4 times as many red buttons as blue buttons. After removing 415 red buttons and 46 blue buttons, the number of blue buttons is 3 times as much as red buttons. Find the number of red buttons initially.

Help to do step by step and labelled working (no algebra or complicated equation as this is for a primary 5 kid) ! Thank you !

Answer 1

Use a bar to represent the total of red buttons initially.

Divide the bar into 4 even parts, then one part is equal to the total of blue buttons initially.

Remove 46 from the total of blue buttons, 415 from the total of red buttons, according to what are given, we have the following relationship:

Add three "415" parts together in another graph. You can find

3 x 415 - 46 is 11 times of the total of blue buttons.

Therefore, total of blue button = (3 x 415 -46)/11 = 109.

Then, total of red buttons = 4 x 109 = 436.

Answer 2

This way is more complicated than using algebra, but I hope it is something that might be appropriate for this level of student.

If we remove 46 blue buttons, for the red buttons to still be 4 times as much, we would need to remove 4 * 46 = 184

However, we remove 415, or 415 - 184 = 231 more.

By removing 231 extra reds, we go from having 4 times as much to 3 times as much. This means that we removed an amount extra equal to the number of blues at this point.

Thus, we end with 231 blues.

Then, we started with 231 + 46 = 277 blues, and 4 * 277 = 1108 reds.

As a check, 1108 - 415 = 693

277 - 46 = 231

231 * 3 = 693

If we are using one variable algebra, we would say

red = 4 blue

4 blue - 415 = (blue - 46) * 3

4 blue - 415 = 3 blue - 138

1 blue = 415 - 138

blue = 277

red = 4 blue = 1108