Respuesta :
Answer:
a) [tex]\left \{ {{0.38x+1.56y=24.80} \atop {x+y=28}} \right.[/tex]
b) 12 blocks and 16 bricks.
Step-by-step explanation:
Let x represent the number of bricks and y represent the number of blocks. Each brick costs $0.38; this gives us the expression 0.38x. Each block costs $1.56; this gives us the expression 1.56y. Together they totaled $24.80; this gives us the equation
0.38x + 1.56y = 24.80
We also know that the number of bricks, x, added to the number of blocks, y, totaled 28; this gives us
x + y = 28
To solve this, we will use substitution. First we will isolate x in the second equation by subtracting y from each side:
x + y = 28
x + y - y = 28 - y
x = 28 - y
Now we substitute this in place of x in the first equation:
0.38(28 - y) + 1.56y = 24.80
Using the distributive property, we have
0.38(28) - 0.38(y) + 1.56y = 24.80
10.64 - 0.38y + 1.56y = 24.80
Combining like terms gives us
10.64 + 1.18y = 24.80
Subtract 10.64 from each side:
10.64 + 1.18y - 10.64 = 24.80 - 10.64
1.18y = 14.16
Divide both sides by 1.18:
1.18y/1.18 = 14.16/1.18
y = 12
There were 12 blocks sold.
Substituting this into the second equation gives us
x + 12 = 28
Subtract 12 from each side:
x + 12 - 12 = 28 - 12
x = 16
There were 16 bricks sold.
