Two numbers are in the ratio 4:1. Their sum is 60. What is the largest number?

Answer 1

Assigning one number a variable and solving is an accurate, efficient strategy. Another way to think about it is with a table ... like this:

1st # 2nd # Total

1 4 5

2 8 10

3 12 15

I'm simply picking a number, then multiplying it by 4 (1:4), and then keeping track of the total. You could continue with the table until you get a total of 60 - and that will tell you your two numbers.

Or, you could make educated guesses until you get closer and closer ...

1st # 2nd # Total

10 40 50

("Close - My number needs to be a little bit bigger!")

1st # 2nd # Total

15 60 75

("Too much!")

You know your smaller number needs to be somewhere between 10 and 15 ...

A table like this can be a great tool for organizing educated guesses and number relationships, as you're getting a better grasp of algebraic thinking!

Answer 2

4x + 1x = 60

5x = 60

x = 12

4x = 48