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Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for 3535 $\$, then took 55 hours of group snowboarding lessons. Victor paid 175175 $\$ in all.\newlineWhich equation can you use to find how much Snowy Ridge charges, xx, for each hour of group snowboarding lessons?\newlineChoices:\newline(A) 5(x+35)=1755(x + 35) = 175\newline(B) 5x+35=1755x + 35 = 175\newline(C) 35(x+5)=17535(x + 5) = 175\newline(D) 35x+5=17535x + 5 = 175\newlineHow much does Snowy Ridge charge for each hour of group snowboarding lessons?\newline____ $\$

Full solution

Q. Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for 3535 $\$, then took 55 hours of group snowboarding lessons. Victor paid 175175 $\$ in all.\newlineWhich equation can you use to find how much Snowy Ridge charges, xx, for each hour of group snowboarding lessons?\newlineChoices:\newline(A) 5(x+35)=1755(x + 35) = 175\newline(B) 5x+35=1755x + 35 = 175\newline(C) 35(x+5)=17535(x + 5) = 175\newline(D) 35x+5=17535x + 5 = 175\newlineHow much does Snowy Ridge charge for each hour of group snowboarding lessons?\newline____ $\$
  1. Understand the problem: Understand the problem.\newlineVictor paid a total of $175\$175 for renting a snowboard and for 55 hours of group snowboarding lessons. We need to find the cost per hour for the lessons, which we will call xx. The cost of renting the snowboard is a one-time fee of $35\$35.
  2. Set up the equation: Set up the equation.\newlineThe total cost is the sum of the one-time snowboard rental fee and the cost of the lessons. The cost of the lessons is the number of hours times the cost per hour 5×x5 \times x. So the equation should represent the total cost as the sum of the rental fee and the cost of the lessons.
  3. Choose the correct equation: Choose the correct equation from the choices.\newlineThe correct equation should have the rental fee added to the product of the number of hours and the cost per hour. This matches choice (B) 5x+35=1755x + 35 = 175, where 5x5x represents the total cost of the lessons and 3535 represents the cost of the snowboard rental.
  4. Solve the equation for x: Solve the equation for x.\newlineSubtract 3535 from both sides of the equation to isolate the term with xx.\newline5x+3535=175355x + 35 - 35 = 175 - 35\newline5x=1405x = 140\newlineNow, divide both sides by 55 to solve for xx.\newline5x5=1405\frac{5x}{5} = \frac{140}{5}\newlinex=28x = 28
  5. Verify the solution: Verify the solution.\newlineMultiply the cost per hour by the number of hours and add the rental fee to ensure it equals the total cost.\newline5×28+35=140+35=1755 \times 28 + 35 = 140 + 35 = 175\newlineThis matches the total cost Victor paid, so the solution is correct.