Question

Five times the number of test tubes in a school’s chemistry lab exceeds three times the number of beakers it has by 660. The sum of two times the number of test tubes and five times the number of beakers is 450.
If b is the number of beakers and t is the number of test tubes, the system of linear equations representing this situation is .
The number of beakers in the school’s lab is , and the number of test tubes in the school’s lab is .

Answer 1

$\left\{\begin{array}{ccc}5t-3b=660&|multiply\ both\ sides\ by\ 2\\2t+5b=450&|multiply\ both\ sides\ by\ (-5)\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}10t-6b=1320\\-10t-25b=-2250\end{array}\right}\\.\ \ \ \ \ \ -31b=-930\ \ \ \ |divide\ both\ sides\ by\ (-31)\\.\ \ \ \ \ \ \ \ \ \ \ \boxed{b=30}\\\\subtitute\ the\ value\ of\ b\ to\ the\ second\ equation:\\\\2t+5\cdot30=450\\2t+150=450\ \ \ \ |subtract\ 150\ from\ both\ sides\\2t=300\ \ \ \ \ |divide\ both\ sides\ by\ 2\\\boxed{t=150}$

Answer:
The number of beakers in the school’s lab is 30, and the number of test tubes in the school’s lab is 150.