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Problem A:

I am thinking of two numbers. When I add the numbers, the answer is 10. When I subtract them, the difference is 2. What are the numbers:

Possible Numbers:

a) 5 and 5

5 + 5 = 10

5 - 5 = 2 X

b) 8 + 2 = 10 √

8 - 2 = 2 X

c) 6 + 4 = 10 √

6 - 4 = 2 √

First addend: x (also the minuend)

Second addend: y (also the subtrahend)

Equation A: x + y = 10 Equation B: x - y = 2

Solution:

x + y = 10

y = 10 - x (use 10-x as subtrahend, instead of y)

Substitute 10 -x to y in Equation B:

x - (10-x) = 2

x + (-10) + x = 2 (Rule in subtraction of integers: Change the sign

each term in the subtrahend, then proceed to

addition.)

x + x - 10 = 2

2x = 2 + 10

2x/2 = 12

First addend: x =

Second added: 10-x ⇒ 10-6 =

Maine gave Lola Nidora a bouquet of 24 flowers. The bouquet was made up of roses, carnations, and daisies. There were twice as many carnations as roses, and three times as many daisies as roses. How many each kind of flower were in the bouquet?

Roses: 1

Carnations: 2 (1) ⇒ twice as many as roses

Daisies: 3 (1) ⇒ thrice as many as roses

The ratio is 1 : 2 : 3

Guesses:

1 + 2 + 3 = 24 X

2 + 4 + 6 = 24 X

3 + 6 + 9 = 24 X

Roses: x

Carnations: 2x

Daisies: 3x

Total Flowers: 24

Solution:

x + 2x + 3x = 24

6x = 24

6x/6 = 24/6

x = 4

The number of flowers for each kind:

Roses: x =

Carnations: 2x = 2 (4) =

Daisies: 3x = 3 (4) =