Ceasars sells whole chicken dinners for $12 and 1/2 chicken dinners for $8. Yesterday they sold a total of 400 dinners and took in $4200. How many of each size dinner were sold?
Let a = whole chicken dinners and b = 1/2 dinners
4200 = 12a + 8b, 400 = a + b
rearrange one of the equations 400 - b = a and substitute into the other and solve.
4200 = 12(400-b) + 8b
4200 = 4800 -12b + 8b
4200 = 4800 -4b
4b = 4800-4200
4b = 600
4b/4 = 600/4
b = 150 of the 1/2 dinners were sold, now solve for a
400 - b = a
400 - (150) = a
250 = a
check
4200 = 12a + 8b
4200 = 12(250) + 8(150)
4200 = 3000 + 1200