Question

Precious and Jia are members of different debate clubs. Precious's debate club costs $39.16 each year and $7.65 per visit. Jia's debate club costs $55.69 each year and $7.08 per visit. Last year they both spent the same amount of money on their debate clubs AND visited the same number of times. How many times did they visit their club?

Answer 1

`\bf\implies`29 times they visit their club.

Explanation:

Step 1) : Based on the given conditions, formulate:

`\bf \longrightarrow{39.16 + 7.65x = 55.69 + 7.08x}`

Step 2) : Solve the equation

`\bf \longrightarrow{39.16 + 7.65x = 55.69 + 7.08x}`

• Rearrange variables to the left side of the equation

`\bf \longrightarrow{7.65x - 7.08x= 55.69 - 39.16}`

• Combine like terms

`\bf \longrightarrow{0.57x= 55.69 - 39.16}`

• Calculate the sum or difference

`\bf \longrightarrow{0.57x= 16.53}`

• Divide both sides of the equation by the coefficient of variable

`\bf \longrightarrow{x= (16.53)/(0.57) }`

• Multiply both the numerator and denominator with the same integer

`\bf \longrightarrow{x= (1653)/(57) }`

• Cross out the common factor

`\bf \longrightarrow{x= 29 }`

Therefore, 29 times they visit their club.