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1) The three angles in a triangle are in the ratio of 2:3:4. Find the measure of each angle.

Let the ratio = x

As in the triangle, sum of all the three angles = 180

2x + 3x + 4x = 180

9x = 180

X = 20

Each angle,

2x = 2( 20) = 40

3x = 3(20) = 60

4x = 4(20) = 80

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2) The sum of 3 consecutive even numbers is 78. Find the numbers.

Let the 3 consecutive even numbers are x, x+2 and x+4.

Therefore,

x + (x + 2) + (x + 4) = 78

Or 3x + 6 = 78

Or 3x = 78 – 6 = 72

Or x = 24 (Divide both sides by 3)

So the three numbers are 24,26,18.

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3) There are 650 students in a school. If the number of girls is 106 more than the boys, how many boys are there in the school?

Let the number of boys = x

Then, number of girls = x + 106

x + (x + 106) = 650 (Given in the question)

Or 2x + 106 = 650

Or 2x = 650 – 106 = 544

Or x = 272

Hence, the number of boys = 272

And, the number of girls = (x + 106)

= 272 + 106

= 378

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4) I have a total of $300 in coins of denomination $1, $2 and $5. The number of $2 coins is 3 times the number of $5 coins. The total number of coins is 160. How many coins of each denomination are with me?

Let $5 coin = x

∴ $2 coins = 3x

Total number of coins = 160

So, $1 coin = 160 - (x +3x)= 160 -4x

Total money = $300

∴ 5(x) + 2(3x) + 1(160 -4x)=300

⇒ 5x + 6x + 160 - 4x = 300

⇒ 11x -4x + 160 =300

⇒ 7x + 160 =300

⇒ 7x = 300 -160

⇒ 7x = 140

So, $5 coins are 20

$2 coins = 3x = 3(20)=60

$1 coins = 160 -(20 + 60)

$1 coins = 80

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