I NEED HELP PLEASE I NEED HELP PLEASE
I NEED HELP PLEASE
I NEED HELP PLEASE
I NEED HELP PLEASE
I NEED HELP PLEASE!!!

1. The width of a rectangle is 5 cm shorter than twice the length. The perimeter is 62 cm. State the
dimensions of this rectangle. (5A, 3C)
2. Stephanie is 3 years older than twice her brother’s age. Two years ago the sum of their ages was 14.
How old will they be next year? (5A, 3C)
3. Find three consecutive integers such that the sum of the smallest and twice the middle integer is 16
more than the largest integer.

1. W=19, L=12

2. Next year Stephanie will be 14 and her Brother will be 6

3. 8, 9, 10

Step-by-step explanation:

1.

(a) W = 2L -5 => W - 2L = -5

(b) 2W + 2L = 62

Making (a)+(b):

3W = 57 => W = 19

from (a): L = (W+5)/2 = 12

2.

Today: S = 2B + 3 => S - 2B = 3 (a),

where S and B are Stephanie and Brother current age

2 years ago: (S-2) + (B-2) = 14,

so S + B = 14 + 4

S + B = 18 (b)

(a) - (b):

-3B = -15 => B = 5

from (a) S = 13

Verification:

2 years ago Stephanie was 11 and Brother was 3, the sum was 14, ok.

Next year Stephanie will be 14 and her Brother will be 6

3. We will find integers: s, m and b:

they are consecutive, so:

m = s+1

b = m+1 = s+2

and:::

s + 2m = b + 16 (a)

In (a) let's express all in terms of s:

s + 2(s+1) = s+2 + 16 =>

2s + 2 = 2 + 16 => s = 8, m=9, b=10

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: