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A set of children’s blocks contains three shapes: long, flats, and cubes. There are three times as many longs as cubes and 30 fewer flats than longs. if there are 600 blocks in all how many Long’s are there

Respuesta :

Answer:

There are 270 longs

Step-by-step explanation:

Equations

We must write the problem into a mathematical model that allows us to apply the properties of basic algebra and solve for the variable which must be adequately set up.

We have three unknowns: the number of long blocks, flats blocks, and cubes. The conditions are given:

  • There are three times as many longs as cubes
  • There are 30 fewer flats than longs.
  • There are 600 blocks in all

For the equation to be easier solved, let's set the variable as the number of cubes:

x = number of cubes

Considering the first condition, we have

3x = number of longs

3x-30 = number of flats

And finally:

[tex]x + 3x+3x-30=600[/tex]

Joining like terms:

[tex]7x=630[/tex]

Solving for x

[tex]\displaystyle x=\frac{630}{7}=90[/tex]

Therefore, there are 3x = 3*(90) = 270 longs

Answer: there are 270 longs

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