System of Equations

Let x be the number of white hydrangeas and let y be the number of pink hydrangeas

So, in the first bed,  x + y = 45

And we want 2 times the number of white hydrangeas in the second bed as the first = 2x and 3 times the number of pink hydrangeas as in the first = 3y   so    2x + 3y = 120

Using the first equation, we can solve for y  by subtracting x from both sides  so   y = 45 - x

And substituting this for y in the second equation, we have

2x + 3(45 - x) = 120    simplify

2x + 135 - 3x = 120

-x + 135 = 120     subtract 135 from each side

-x = -15               multiply both sides by -1

x = 15    and y = 45- 15 = 30

So.....there are 15 white hydrangeas in the first bed and we need twice this number in the second bed = 30....so that's 45 total white hydrangeas

And there are 30 pink hydrangeas in the first bed and we need three times this many in the second bed = 90So that's a total of 120 pink hydranges

Let w be the number of white hydrangeas in the first bed and p be the number of pink ones.

Then

w + p = 45           1st bed       so  p = 45 - w

2w + 3p = 120      2nd bed     or  2w +3(45 - w) = 120   so  -w + 135 = 120  or w = 15

Since p = 45 - w  then p = 30

Total number of whites = 3w = 45

Total number of pinks = 4p = 120

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