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3 years ago

Translate the sentence into an equation.

Mathematics

1 answer:

Luba_88 [7]3 years ago

3 0

Answer:

The expression of the given statement is 8 y - 2 = 6.

Step-by-step explanation:

Here, let the unknown number = y

Now, product of y and 8 = 8 times y = 8 y

Also, two less than the product = Product - 2

So, two less than the product of 8 and y = 8 y - 2

Now, this above expression is equivalent to 6.

⇒8 y - 2 = 6

Hence the expression of the given statement is 8 y - 2 = 6.

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In the 75th Congress (1937−1939) there were in the Senate 75 Democrats, 17 Republicans, and 4 members of other parties. Suppose

never [62]

Answer:

48 Democrats

14 Republicans

2 members of other parties

Step-by-step explanation:

This can be solved by a system of equations.

I am going to say that:

x is the number of democrats that voted for the bill

ax is the number of democrats that voted against the bill

y is the number of republicans that voted for the bill

ay is the number of republicans that voted against the bill

z is the number of members of other parties that voted for the bill

az is the number of members of other parties that voted against the bill.

Now we use the informations the exercise gives us so we can build the system.

There were 75 democrats, so:

$x + ax = 75$

17 republicans, so:

$y + ay = 17$

4 members of other parties, so:

$z + az = 4$

A bill passed the Senate with 32 more votes in favor than against, so

$x + y + z = 32 + ax + ay + az$

Three times as many Democrats voting in favor as non-Democrats voting in favor

$x = 3(y + z)$

And 34 more Democrats voting in favor than Republicans voting in favor:

$x = y + 34$

The easiest equation to replace is this:

$x + y + z = 32 + ax + ay + az$

The first step is writing everything just with x, y and z, so:

$x + ax = 75$

$ax = 75 - x$

-------------

$y + ay = 17$

$ay = 17 - y$

------------

$z + az = 4$

$az = 4 - z$

So we have:

$x + y + z = 32 + ax + ay + az$

$x + y + z = 32 + 75 - x + 17 - y + 4 - z$

$2x + 2y + 2x = 128$

Dividing by 2

$x + y + z = 64$

We also have that

$x = y + 34$

$y + 34 + y + z = 64$

$2y + z = 30$

And

$x = 3(y + z)$

$3z = x - 3y$

$3z = y + 34 - 3y$

$3z = 34 - 2y$

$z = \frac{34 - 2y}{3}$ 7

So:

$2y + z = 30$

$2y + \frac{34 - 2y}{3} = 30$

$6y + 34 - 2y = 90$

$4y = 56$

$y = 14$

14 republicans voted in favor of the bill.

$2y + z = 30$

$2(14) + z = 30$

$z = 2$

2 members of other parties voted in favor of the bill.

$x = y + 34$

$x = 14 + 34$

$x = 48$

48 democrats voted in favor of the bill

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Answer:

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Step-by-step explanation:

That's the correct answer :)

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