Vera is on her school's track and field term. In a partice long-jump competition against her temmates, she gets 5 points for landing over the nearer line and 10 points for landing over the more distant line. She gets a total of 7 jumps and lands x times over the more distant line and the rest of the times over the nearer line. Which of the following equations represents the relationship between Vara's total score, y, and the number of times she lands over the more distant line, x ?

Options

A. `y =10x`
B. `y=5x+ 35`
C. `y=10x+5`
D. `y=70-5x`

Answer

B

Explanation

The key to answering this question is determining how many jumps land across each line. If Vera gets 7 jumps total and x jumps land over the more distant line, then the rest, or `7-x,` must land over the near line. Now, write the expression in words: points per distant line (10) times number of jumps landing over the distant line (x), plus points per near line (5) times number of jumps landing over the near line `(7-x).` Next, translate the words into numbers, variables, and opertions: `10x+5 (7-x).` This is not one of the answer choices, so simplify the expression by distributing the 5 and combining like terms:
`10x+ 5 (7-x) =10x + 35-5x=5x+35,` so the equation is `y =5x+ 35.` (B) is correct.