Question

Martina is currently 16 years older than her cousin Joey. In 5 years she will be 3 times as old as Joey. Use this information to answer the following questions. If you let x represent Joey’s current age, what expression can you use to represent Martina’s current age? Based on your answer to part a, what expression represents Joey’s age in 5 years? What expression represents Martina’s age in 5 years? What equation can you write based on the information given? What is Joey’s current age? What is Martina’s current age?

Answer 1

m=martina's age now
x=joe's age now

m is 16 older than x means
m=16+x


in 5 years (m+5 and x+5) she will be 3 times as old a joey
m+5=3(x+5)

so
we have
m=16+x
m+5=3(x+5)



a.
m=16+x

b.
x+5
m+5

c.
m=16+x
m+5=3(x+5)

d.
solving
sub 16+x for m
16+x+5=3(x+5)
distribute and add like terms
21+x=3x+15
minus x both sides
21=2x+15
minus 15 both sides
6=2x
divide by 2
3=x

m=16+x
m=16+3
m=19

joey is 3 and martina is 19

Answer 2

m = j + 16
m + 5 = 3j
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put the system of linear equations into standard form
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m - j = 16
m - 3j = -5
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x - y = 16
x - 3y = -5

so now that you have your equations formed, just solve.

x - y = 16 , which means that x = y + 16
substitute for x in the second equation :

Hope this helps