Question

Ava travels twice as far as Aaliyah when going to camp. Serenity travels as far as Ava and Aaliyah together. Mrs. Scott travels 3 times as far as Ava. In total, all four travel 888 miles to camp. How far does each travel to camp?

Answer 1

Distance traveled by Ava = 148 miles

Distance traveled by Aaliyah = 74 miles

Distance traveled by Mrs. Scott = 444 miles

Distance traveled by Serenity = 222 miles

Explanation:

Distance traveled by Ava = Av

Distance traveled by Aaliyah = Aa

Distance traveled by Mrs. Scott = Sc

Distance traveled by Serenity = Se

The following set of equations can be deduced from the information provided:

`Av = 2Aa\\Se = Av+Aa\\Sc = 3Av\\Av+Aa+Se+Sc=888`

Solving the linear system:

`Av = 2Aa\\Se = 2Aa+Aa=3Aa\\Sc = 3*2Aa=6Aa\\2Aa+Aa+3Aa+6Aa=888\\Aa=74\ miles\\\\Av=2*74=148\ miles\\Se = 74+148=222\ miles\\Sc=3*148= 444\ miles`

The distances traveled by each person are:

Distance traveled by Ava = 148 miles

Distance traveled by Aaliyah = 74 miles

Distance traveled by Mrs. Scott = 444 miles

Distance traveled by Serenity = 222 miles