Question

A total of $1680 is to be given as cash prizes to 7 students of a school for their
overall academic performances. If each price is $30 less than its preceding prize, find
the value of each prize.

Answer 1

Answer: the values of each prize are

$330,$300,$270,$240,$210,$180,$150.

Given:

• sum of total prize money=$1680
• number of students=7
• each prize is $30 less than the preceding prize

  The above conditions are in the form of an Arithmetic Progression(AP)

with sum of series($S_{n}$) 1680 , 7 terms(n) in the AP and common ratio(d)=30

Let the first term of the AP be 'a'.

$S_{n}=\frac{n}{2}[2a+(n-1)*d]$

$1680=\frac{7}{2}[2a+(7-1)*30] \\1680=\frac{7}{2} [2a+180]\\1680*2=7*(2a+180)\\3360=14a+1260\\14a=3360-1260\\14a=2100\\a=2100/14\\a=150$

The 7th award is $150

The 6th award is $(150+30)=$180

The 5th award is $(180+30)=$210

The 4th award is $(210+30)=$240

The 3rd award is $(240+30)=$270

The 2nd award is $(270+30)=$300

The 1st award is $(300+30)=$330

Reference: To know more about Arithmetic Progressions :

https://brainly.com/question/13989292

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