# 11. meg is 6 years older than victor. meg's age is 2 years less than five times victor's age. the equations

###### Question:

meg is 6 years older than victor. meg's age is 2 years less than five times victor's age. the equations below model the relationship between meg's age (m) and victor's age (v):

m = v + 6

m = 5v – 2

which is a possible correct method to find meg's and victor's ages? (5 points)

solve m + 6 = 5m – 2 to find the value of m.

write the points where the graphs of the equations intersect the x axis.

solve v + 6 = 5v – 2 to find the value of v.

write the points where the graphs of the equations intersect the y axis.

12.

the distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below:

car a

y = 60x + 10

car b

y = 40x + 70

after how many hours will the two cars be at the same distance from their starting point and what will that distance be? (5 points)

2 hours, 150 miles

2 hours, 190 miles

3 hours, 150 miles

3 hours, 190 miles

## Answers

11. solve v + 6 = 5v - 2 for v <==

12. 60x + 10 = 40x + 70

20x = 60

x = 3same at 3 hrs190 miles <==

11. since both equations = m, then make both equations = each other so you would have v+6 = 5v-2 and solve for v

12. just like in 11 make both equations = each other and solve for x

60x+10 =40x+70

60x = 40x+60

20x =60

x = 60/20 = 3 hours

now use that as x to calculate miles

60(3) +10 = 190

3 hours, 190 miles

The correct option is

(C) Solve v + 6 = 5v − 2 to find the value of v.

Step-by-step explanation: Given that Meg is 6 years older than Victor. Meg's age is 2 years less than five times Victor's age.

The following equations model the relationship between Meg's age (m) and Victor's age (v):

m = v + 6

m = 5v − 2

We are to select the possible correct method to find Meg's and Victor's age.

Since both the equations gives the value of m, so it is better to compare both the equations to solve the given system.

That is,

after comparing both the equations, we will get

v + 6 = 5v - 2.

From here, we get the value of v and then substituting this value in any one of the two equations, we will readily find the value of m.

Thus, option (C) is CORRECT.

Since no possible correct method is posted, I will suggest a couple.

Method 1: guess and check

Works well for simple problems involving integers like this one.

Victor's age must be zero or greater than one, say one.

Guess v=1, find m=v+6=7, check m=5v-2=5-2=3 no good.

we need to make v bigger

Guess v=2, find m=v+6=2+6=8, check m=5v-2=5*2-2=8 ✔

So v=2, m=8.

Method 2:

Solve the system of two equations.

since the left-hand sides is m in both equations, and since m=m, we just have to equate the right-hand sides to solve for v.

5v-2=v+6

Solve for v

5v-v = 6+2

4v=8

v=2,

so again, v=2, m=v+6=2+6=8.

A possible correct method to find Meg's and Victor's age is substitution. Another one is elimination.

Let's see our options

A. this is wrong, m and v have been switched

B. this is assuming that one of their ages is 0

C. correct, v+6=m=5v-2, or v+6=5v-2

D. this assumes the other person is 0 years old

answer is C

The first one is correct because the second one is not! The power of process of elimination!

Here is why the 2nd one is incorrect.

V+6=5v-2

Victor is not 6 years older than 2 less than 5 times his own age.

You would use the second way since meg is older than victor and not the other way around