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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) 35(x+5)=17535(x + 5) = 175\newline(B) 35x+5=17535x + 5 = 175\newline(C) 5(x+35)=1755(x + 35) = 175\newline(D) 5x+35=1755x + 35 = 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) 35(x+5)=17535(x + 5) = 175\newline(B) 35x+5=17535x + 5 = 175\newline(C) 5(x+35)=1755(x + 35) = 175\newline(D) 5x+35=1755x + 35 = 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 is represented by xx.
  2. Set up the equation: Set up the equation.\newlineThe total cost is the sum of the fixed cost for renting the snowboard and the variable cost for the lessons. The fixed cost is $35\$35, and the variable cost is 55 times the cost per hour (5x)(5x). So the equation is 35+5x=17535 + 5x = 175.
  3. Identify the correct equation: Identify the correct equation from the choices.\newlineThe correct equation that represents the situation is (D) 5x+35=1755x + 35 = 175.
  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 fixed cost 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.