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Evgen [1.6K]
3 years ago
14

10 11 5(2x + 1) + c(x + d) = 12x - 1 Work out the value of c and the value of d.

Mathematics
1 answer:
Lady bird [3.3K]3 years ago
8 0

Answer:

c = 2, d = - 3

Step-by-step explanation:

Expand and simplify the left side then compare the coefficients of like terms on both sides.

5(2x + 1) + c(x + d) ← distribute parenthesis

10x + 5 + cx + cd

= x(10 + c) + 5 + cd

Compare like terms on both sides, that is

10 + c = 12 ( subtract 10 from both sides )

c = 2

Then

5 + cd = 5 + 2d and

5 + 2d = - 1 ( subtract 5 from both sides )

2d = - 6 ( divide both sides by 2 )

d = - 3

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The mentioned number in the exercise is:

  • <u>362</u>

Step-by-step explanation:

To obtain the mentioned number in the exercise, first you must write the equations you can obtain with it.

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  • y = tens digit
  • z = ones digit

We can write:

  1. x = z + 1 (the hundreds digit is one more than the ones digit).
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Taking into account these data, we can use the third equation and replace it to obtain the number and the value of each digit:

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  • (z + 1) + y + z = 11 (remember x = z + 1)
  • z + 1 + y + z = 11
  • z + z +y + 1 = 11 (we just ordered the equation)
  • 2z + y + 1 = 11 (z + z = 2z)
  • 2z + y = 11 - 1 (we passed the +1 to the other side of the equality to subtract)
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  • z = 8/4
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Now, we know z (the ones digit) is 2, we can use the first equation to obtain the value of x:

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And we'll use the second equation to obtain the value of y (the tens digit):

  • y = 2x
  • y = 2(3)
  • <u>y = 6</u>

Organizing the digits, we obtain the number:

  • Number = xyz
  • <u>Number = 362</u>

As you can see, <em><u>the obtained number is 362</u></em>.

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