Question

7. A sum of 2800 is to be used to award four prizes. If each prize after
the first is 200 less than the preceding prize, find the value of each of
the prizes.​

Answer 1

Solution :

$\bigstar$ We have 4 award prizes that is total sum is 2800.

Let the value of first award prize be Rs.r

A/q

• The value of second award prize be Rs.(r-200)
• The value of third award prize be Rs.(r-2×200)
• The value of fourth award prize be Rs.(r-3×200)

Now;

$\longrightarrow\sf{(1^{st}\:award)+(2^{nd}\:award)+(3^{rd}\:award)+(4^{th}\:award)=2800}\\\\\longrightarrow\sf{r+(r-200)+(r-2\times 200)+(r-3\times 200)=2800}\\\\\longrightarrow\sf{r+r-200+r-400+r-600=2800}\\\\\longrightarrow\sf{4r-1200=2800}\\\\\longrightarrow\sf{4r=2800+1200}\\\\\longrightarrow\sf{4r=4000}\\\\\longrightarrow\sf{r=\cancel{4000/4}}\\\\\longrightarrow\bf{r=Rs.1000}$

Thus;

$\bullet\:\sf{The\:1^{st}\:award\:prize=r=\boxed{\bf{Rs.1000}}}\\\\\bullet\sf{The\:2^{nd}\:award\:prize=(r-200)=(1000-200)=\boxed{\bf{Rs.800}}}\\\\\bullet\sf{The\:3^{rd}\:award\:prize=(r-400)=(1000-400)=\boxed{\bf{Rs.600}}}\\\\\bullet\sf{The\:4^{th}\:award\:prize=(r-600)=(1000-600)=\boxed{\bf{Rs.400}}}$