Question

the xyz act set the standard gauge for country a railroads at 35\frac{16}{21} inches. (see figure.) if the standard gauge in country b is 50\frac{1}{7} inches, how much wider is country bs standard gauge than country as standard gauge?
country bs standard gauge is inches wider than country as standard gauge.
(simplify your answer. type an integer, proper fraction, or mixed number.)

Explanation:

Step1: Convert mixed - numbers to improper fractions

Country A's gauge: $35\frac{16}{21}=\frac{35\times21 + 16}{21}=\frac{735+16}{21}=\frac{751}{21}$ inches. Country B's gauge: $50\frac{1}{7}=\frac{50\times7+1}{7}=\frac{350 + 1}{7}=\frac{351}{7}$ inches.

Step2: Find a common denominator

The common denominator of 21 and 7 is 21. Rewrite $\frac{351}{7}$ with a denominator of 21: $\frac{351}{7}=\frac{351\times3}{7\times3}=\frac{1053}{21}$ inches.

Step3: Subtract the two fractions

$\frac{1053}{21}-\frac{751}{21}=\frac{1053 - 751}{21}=\frac{302}{21}$ inches.

Step4: Convert to a mixed - number

$302\div21 = 14$ with a remainder of 8. So $\frac{302}{21}=14\frac{8}{21}$ inches.

Answer:

$14\frac{8}{21}$