Two brothers are three years apart in their age. the sum of their ages is 17. use a system of equations to find their current age.

The younger brother is 7 years old and the older brother is 10 years old.

Step-by-step explanation:

1. Let x represent the age of the younger brother and y represent the age of the older brother.

Then, if they are three years apart in age, the age of the older brother is given by the age of the younger brother plus 3:

y = x + 3

2. If the sum of their ages is 17, then:

x + y = 17

3. There are many different ways to solve the question from this point onwards, however I will show how we may substitute the first equation into the second as it doesn't require any rearranging of formulas.

Thus, if y = x + 3, then:

x + y = x + (x + 3)

If x + y = 17, then:

x + x + 3 = 17

2x + 3 = 17

2x = 14 (Subtract 3 from each side)

x = 7 (Divide both sides by 2)

Since x represents the age of the younger brother, we now know that he is 7 years old.

4. To find the older brother's age, we simply substitute x = 7 into the first equation:

y = x + 3

y = 7 + 3

y = 10

Therefor, the older brother is 10 years old.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.