Question

there is $175,000 to award. If the money is awarded to 4 students in a ratio of 1 to 2 to 3 to 4, how much will the largest award be?

How would I solve this ?

Answer 1

solve for x

x + 2x + 3x + 4x = 175 000

then evaluate 4x

Answer 2

could you explain why you put it into that equation?

Answer 3

I split the parts into the given ratios of
1 : 2 : 3 : 4 or
x : 2x : 3x : 4x
remember that ratios can be reduced to "lowest terms" by dividing each value by the same number, a common factor.
In the same way I can build up a ratio by myltiplying each term by the same value
e.g.
1:2:3:4
= 5:10:15:20
= 100:200:300:400
or in an infinite number of way.
So I chose x as my multiplier

then the 4 parts must add up to 175 000
x+2x+3x+4x = 175000
10x = 175000
x = 17 500

then 2x = 35 000
3x = 52 500
4x = 70 000

notice that
17500 : 35000:52500:70000
= 175:350:525:700
= 1:2:3:4 and their sum is 175000

Answer 4

ok
thank you