Answer: 14 red, 7 green, 44 blue
Step-by-step explanation:
First, use the letter <em>r</em> as a variable to represent the number of red Legos. The number of green Legos (<em>g</em>) is 7 less than the number of red Legos, or <em>g = r-7.</em> The number of blue Legos (b) is 2 more than 3 times the number of red Legos, or <em>b = 3r+2</em>. The total number of Legos is the number of red + green + blue Legos, which can be represented as <em>65 = r+g+b</em>.
Substitute the equations for g and b in. This should give you a final equation of <em>65 = r+(r-7)+(3r+2)</em>. To solve for the number of <u>red</u> Legos, first add up all of the terms to get <em>65 = 5r-5</em>. Now add 5 to each side (70<em> = 5r</em>). Finally, divide each side by 5 (r = 14).
To find the number of <u>green</u> Legos, substitute the number of red Legos (14) into the equation for the green Legos (<em>g = r-7</em>). This should get you the equation <em>g = 14-7</em> which simplifies to g = 7.
To find the number of <u>blue</u> Legos, substitute the number of red Legos (14) into the equation for the blue Legos (<em>b = 3r+2</em>). This gives you the equation <em>b = (3*14)+2.</em> First, multiply 3 and 14 to get <em>b = 42+2</em>. Finally, add them together to get b = 44.
