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 ?
solve for x
x + 2x + 3x + 4x = 175 000
then evaluate 4x
could you explain why you put it into that equation?
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
ok
thank you
To determine how much the largest award will be, we can break down the ratio and assign it to variables. Let's assign the variables as follows:
Let the smallest ratio be x
The second ratio will be 2x
The third ratio will be 3x
The largest ratio will be 4x
Now, we can create an equation to represent the total sum of the ratios:
x + 2x + 3x + 4x = $175,000
Simplifying, we have:
10x = $175,000
To find the value of x, we divide both sides of the equation by 10:
x = $17,500
Now that we have the value of x, we can determine the largest ratio:
4x = 4 * $17,500 = $70,000
Therefore, the largest award will be $70,000.