Question

Help with these 2 algebra questions!!

1. A number is four more than twice another number. If the difference between the numbers is 27, determine the numbers.

2. Suppose that 2 sides of a triangle are equal and the third side is 10cm greater than each of the other two. the perimeter of the triangle is 100cm. find the length of each side.

Answer 1

1. Let's call the first number "x" and the second number "y". We know that:

x = 4 + 2y (equation 1)

x - y = 27 (equation 2)

We can use equation 1 to substitute x in equation 2:

(4 + 2y) - y = 27

Simplifying the equation:

3y = 23

So the second number is:

y = 23/3

Using equation 1, we can find the first number:

x = 4 + 2(23/3) = 50/3

Therefore, the numbers are 50/3 and 23/3.

2. Let's call the length of the equal sides of the triangle "x" and the length of the third side "y". We know that:

y = x + 10 (equation 1)

2x + y = 100 (equation 2)

We can use equation 1 to substitute y in equation 2:

2x + (x + 10) = 100

Simplifying the equation:

3x = 90

So the length of the equal sides is:

x = 30

Using equation 1, we can find the length of the third side:

y = 30 + 10 = 40

Therefore, the lengths of the sides are 30, 30, and 40.