college algebra linear systems

Question

Last year, Singer A performed one more than two times as many shows during concert tours than Team B. The number of Singer A concert tour shows exceeded the number of shows by Team B by 12. How many concert shows did each perform?

Answer 1

Similarly to the last problem I helped you with, if we let A be the number of shows performed by Singer A and B be the number of shows performed by Singer B, what we're given in the problem translates to 2 equations:

A = 2B + 1 (A performed one more than 2 times as many shows as B)

A = B + 12 (A performed 12 more shows than B)

We'll solve for B first, as that seems easiest:

If we subtract the second equation from the first, we get that A - A = (2B + 1) - (B+12)

If we simplify this we get that 0 = B - 11, so B = 11.

We can now solve for A by plugging into either equation: since A = B +12 and B = 11, A = 11+12 = 23.

So A performed 23 shows and B performed 11 shows.