A yoga studio has two participation plans. For the first plan the cost is $8 per visit for the second plan the cost is $40 per month and $2 per visit write an equation to show the number of visits per month that it would take for the two plans to be equal use x as your variable

Answer 1

To find the number of visits per month at which the two plans cost the same, we can set up an equation based on the costs of each plan.

1. Cost of the first plan (pay-as-you-go):

   • The cost is $8 per visit.
   • If \( x \) is the number of visits, the total cost for this plan can be expressed as: \[ \text{Cost}_{\text{plan 1}} = 8x \]

2. Cost of the second plan (monthly subscription):

   • The cost is $40 per month plus $2 per visit.
   • The total cost for this plan can be expressed as: \[ \text{Cost}_{\text{plan 2}} = 40 + 2x \]

Now, we set the two expressions equal to each other to find the number of visits \( x \) at which both plans cost the same: \[ 8x = 40 + 2x \]

Next, we can solve this equation for \( x \):

1. Subtract \( 2x \) from both sides: \[ 8x - 2x = 40 \] \[ 6x = 40 \]

2. Divide both sides by 6: \[ x = \frac{40}{6} = \frac{20}{3} \approx 6.67 \]

Thus, the number of visits per month that it would take for the two plans to be equal is approximately 6.67 visits. Since you typically can't have a fraction of a visit, it means that for less than about 6.67 visits, Plan 1 would be cheaper, and for more than about 6.67 visits, Plan 2 would be cheaper.