Find the Numbers inside! a) Blue- 5; Red- 15; Green- 12; Orange- 7 b) Blue- 7; Red- 15; Green- 6; Orange- 5 c) Blue- 9; Red- 7; Green- 12; Orange- 15 d) Blue- 7; Red- 9; Green- 19; Orange- 7?

We can solve these equations step by step to find the values of Blue, Red, Green, and Orange.

First, let's solve for one of the colors. We'll start with Blue:

From equation 1, we have:
Blue + Red = 16
=> Blue = 16 - Red [Let's call this equation 5]

Now, substitute equation 5 into equation 2:
(16 - Red) + Green = 26
=> 16 - Red + Green = 26
=> Green - Red = 26 - 16
=> Green - Red = 10 [Let's call this equation 6]

Next, use equations 3 and 4:
Red + Orange = 16 and Green - Orange = 12

These can be rewritten as:
Orange = 16 - Red [Let's call this equation 7]
Green = Orange + 12 [Let's call this equation 8]

Now, substitute equation 7 into equation 8:
Green = (16 - Red) + 12
=> Green = 28 - Red [Let's call this equation 9]

Finally, substitute equation 9 into equation 6:
28 - Red - Red = 10
=> 28 - 2 * Red = 10
=> 2 * Red = 28 - 10
=> 2 * Red = 18
=> Red = 18 / 2
=> Red = 9

Now, we can find the values of the other colors using the value of Red:

From equation 5:
Blue = 16 - 9
=> Blue = 7

From equation 7:
Orange = 16 - 9
=> Orange = 7

From equation 9:
Green = 28 - 9
=> Green = 19

So, the values are:

Blue = 7
Red = 9
Green = 19
Orange = 7

 

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