Question

50 POINTS!!! Urgent, Extremely Confused!

So far, Marta has correctly predicted the winner of 6 out of 13 football games. She wants to know how many consecutive games she would have to predict correctly to raise the percent of correct predictions to 65%.

a. Write an equation to represent this situation.
b. Solve the equation. !Show all steps!
c. Answer the question. How many consecutive games must she predict correctly to raise her percent to 65%?

Answer 1

Required Answer:-

Marta predicted correctly 6 out of 13 football games .

• We need to find first Her's Current percentage

`\longrightarrow`
`\sf {\frac {6}{13}}* 100`

`\longrightarrow`
`\sf {\frac {600}{13}}`

`\longrightarrow`
`\sf 46.15\%`

• Now We need to add x in both denominator and numerator

`\longrightarrow`
`\sf {\frac {6+x}{13+x}}={\frac {65}{100}}`

• Simplify
• use cross multiplication method

`\longrightarrow`
`\sf 100 (6+x)=65 (13+x)`

`\longrightarrow`
`\sf 600+100x=845+65x`

`\longrightarrow`
`\sf 100x-65x=845-600`

`\longrightarrow`
`\sf 35x=245`

`\longrightarrow`
`\sf x={(245)/(35)}`

`\longrightarrow`
`\sf x=7`

• So the new rational number

`\longrightarrow`
`\sf {\frac {6+x}{13+x}}`

`\longrightarrow`
`\sf {\frac {6+7}{13+7}}`

`\longrightarrow`
`\sf {\frac {13}{20}}`

`\therefore` Marti needs to predict more 13 games out of 20 to raise her percentage to 65%.