Patanna bought some red and blue bricks. She bought a total or 100 bricks. The red bricks cost $5 each and the blue bricks cost $7 each. She spent a total of $560. How many red bricks and how many blue bricks did she buy?

Let...

x=the number of red bricks

y=the number of blue bricks

Since she bought a total of 100 bricks... x+y=100.

Because the total cost is $560... 5x+7y=560.

Using these two equations, we can use the substitution method to solve for x and y.

x+y=100 > x=100-y

        subtract y on both sides

Because x=100-y...

                                                                  this is x

5x+7y=560 (second equation) equals 5( 100 - y )+7y=560  

This equation we created has only one variable so we can solve it.

5(100-y)+7y=560

500-5y+7y=560

2y+500=560

2y=60

y=30 blue bricks

Because x=100-y... x=100-30=70 red bricks.

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