Question

Peter is 2 years older than Winnie. Peter's age is 16 years less than seven times Winnie's age. The equations below model the relationship between Peter's Age (p) and Winnie's age (w):
p=w+2
p=7w-16

Which is a possible correct method to find Peter's and Winnie's ages?

A. Solve w+2 = 7w-16 to find the value of w
B. Solve p+2 =7p-16 to find the value of p
C. Write the points where the graphs of the equations intersect the x axis
D. Write the points where the graphs of the equations intersect the y axis

Answer 1

Given equations:
P=w+2
p=7w-16
Compare both equations
7w-16=w+2
Add 16 to both sides.
7w=w+18
Subtract w from both sides.
6w=18
Divide both sides by 6.
w=3, which is the age of Winnie.
Now Peter's age=3+2=5 years

Option A is the correct method to find the age of Peter and Winnie.

Answer 2

Answer:

A. Solve w+2 = 7w-16 to find the value of w.

Step-by-step explanation:

Here p represents the age of Peter and w represents the age of Winnie,

Given,

Peter is 2 years older than Winnie.

⇒ p = w + 2 -----(1)

Also, Peter's age is 16 years less than seven times Winnie's age.

⇒ p = 7w - 16 -----(2),

By equating right sides of equation (1) and (2),

We get,

w + 2 = 7w - 16,

Since, this equation is only in the variable w,

Thus, we can find the value of w with help of the above equation,

After putting this value in either of equation (1) or (2),

We can find the value of p.

Hence, option A is correct.

Note : From equation (1) and (2),

w = p - 2 and $w=\frac{p+16}{7}$

$\implies p-2=\frac{p+16}{7}$

⇒ Option B is incorrect.

Now, let x represents w and y represents p in the graph,

Then, the solution will be the intersection point of lines y=x+2 and y=7x-16,

Which is shown below,

⇒ Options C and D are incorrect.