Question

Vera is on her Schools track and field team. In a practice long Jump, she has to make a total of 7 jumps. For each jump over the closer line she gets 5 points and for each jump over the farther line she gets 10 points. If she makes x jumps over the farther line and the rest of times over the closer line, which of the following function describes Vera’s score
[a] $f\left( x \right)=10x$
[b] $f\left( x \right)=5x+35$
[c] $f\left( x \right)=10x+5$
[d] $f\left( x \right)=70-5x$

Answer 1

Hint: Find the number of points Vera gets by landing over the farther line and the number of points vera gets by landing on the closer line. Hence find the total number of points Vera gets by adding the points she got in each case and simplify the resulting algebraic expression. Hence determine which of the options is correct. Verify your answer by finding the answer for a particular value of x.

Complete step by step answer:
The number of times Vera lands over the farther lines is x.
For each jump over the farther line Vera gets 10 points.
Hence the number of points she got by landing over the farther line is $10x$
Also, since total number of Jumps is 7, the number of time Vera Jumps over the closer line is 7-x
For each jump over the farther line she gets 5 points.
Hence the number of points she gets by Jumping over the closer line is $5\left( 7-x \right)$
We know that multiplication distributes over subtraction, i.e. a(b-c) = ab-ac
Hence, we have
The number of points Vera gets by Jumping over the closer line is $5\left( 7 \right)-5x=35-5x$
Hence the total number of points Vera gets is $10x+35-5x=35+5x$
Hence, we have
$f\left( x \right)=5x+35$

So, the correct answer is “Option B”.

Note: [1] Verification:
Suppose Vera makes 2 Jumps over the farther line and 5 Jumps over the closer line (i.e. x = 2). Total number of points Vera gets is $5\left( 5 \right)+2\left( 10 \right)=25+20=45$
Also, we have $f\left( 2 \right)=5\left( 2 \right)+35=10+35=45$
Hence our solution is verified to be correct.