Answer:
a.
[tex]\left\{\begin{array}{l}x+y=40\\ \\7x+4y=193\end{array}\right.[/tex]
b. 11 red bricks
Step-by-step explanation:
Let x be the number of red bricks and y be the number of grey bricks.
1. Monica purchased 40 bricks, so
[tex]x+y=40[/tex]
2. If she purchased the red bricks for $7 each, then x red bricks cost $7x. If the gray bricks are for $4 each, then y bricks cost $4y. In total, all bricks cost $(7x + 4y) that is $193. Hence,
[tex]7x+4y=193[/tex]
a. The system of two equations is
[tex]\left\{\begin{array}{l}x+y=40\\ \\7x+4y=193\end{array}\right.[/tex]
b. From the first equation:
[tex]y=40-x[/tex]
Substitute it into the second equation:
[tex]7(40-y)+4y=193\\ \\280-7y+4y=193\\ \\-7y+4y=193-280\\ \\-3y=-87\\ \\3y=87\\ \\y=29\\ \\x=40-29=11[/tex]
Monica purshased 11 red bricks and 29 grey bricks.
