There are only blue pens, green pens and red pens in a box. The ratio of the number of blue pens to the number of green pens is 2:5
The ratio of the number of green pens to the number of red pens is 4:1
There are less than 100 pens in the box.
What is the greatest possible number of red pens in the box?

  15 red pens

Step-by-step explanation:

We can multiply the first ratio by 4 to give 20 as the number representing green pens:

  blue : green = 8 : 20

We can multiply the second ratio by 5 to give 20 as the number representing green pens:

  green : red = 20 : 5

Then the combined ratios are ...

  blue : green : red = 8 : 20 : 5 . . . . . . . . . total of 33 "ratio units"

If each "ratio unit" represents 3 pens, then there would be a total of 99 pens in the box. That would mean there are at most 5×3 = 15 red pens.

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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