club A charge $11 for membership and $11 monthly. Club B charge $27 membership and $7 monthly. After how many many months will they charge the same? How much for each?
Let [latex]m[/latex] be the number of months. Since Club A charges $11 only one time and charges $11 per month, the total charge after [latex]m[/latex] months is [latex]\$11 + \$11m[/latex]. Similarly, the total charge after [latex]m[/latex] months for Club B is [latex]\$27 + \$7m[/latex]. Since we want to find after how many months the two clubs charge the same amount, we can set those two expressions equal to each other and solve: [latex]\$11 + \$11m = \$27 + \$7m[/latex] [latex]\$4m = \$16[/latex] [latex]\bf m = 4[/latex] So, Club A and Club B will charge the same amount after 4 months. To find how much they charge, just plug [latex]m[/latex] back into one of the original equations: [latex]\$11 + \$11m = \$11 + \$11(4) = \bf \$55[/latex]