On a three-day hike, matthew hiked twice as much miles on the first day as on the second day. on the third day he hiked 5 miles. carlos hikes 5 miles on the first day and three times as many miles on the second day as on the third day. if carlos hiked 4 miles on the third day, which boy hiked a greater total distance? justify your answer using mathematics in the box below.

Distance hiked by Matthew

Matthew hiked twice as much miles on the first day as on the second day. On the third day he hiked 5 miles.

Distance traveled by Matthew on first day =2 x miles

Distance traveled by Matthew on second day = x miles

Distance traveled by Matthew on third day =5 miles

Total,Distance traveled by Matthew on total of three days =2 x+x+5=(3 x+5) miles

Distance hiked by Carlos

Carlos hikes 5 miles on the first day and three times as many miles on the second day as on the third day.   Carlos hiked 4 miles on the third day.

Distance traveled by Carlos on first day= 5 miles

Distance traveled by Carlos on third day= 4 miles

Distance traveled by Carlos on Second day= 4 ×3=12 miles

Total Distance  traveled by Carlos on total of three days= 5 +12+4=21 miles

As, Distance traveled by Matthews=(3 x+5) miles, on first and second day is a variable Quantity.So, we can't compare .

Three cases arises

1. If distance traveled by Matthews is greater than distance traveled by Carlos, then value of x is,

3 x +5 > 21

3 x >16

x>

2. If distance traveled by Matthews is less than distance traveled by Carlos, then value of x is,

x <  

3. If distance traveled by Matthews is equal to distance traveled by Carlos, then value of x is,

x=  

So, we can't say who traveled greater distance between Matthew and Carlos.

180

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