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3 years ago

10

What is the solution to 8(2x + 3) = 48?

1 answer:

Tom [10]3 years ago

6 0

You have to start by using the distributive property. So you take the number next to the parentheses which is “8” and you multiply it with “2x”. This gives you “16x”. Then you multiply “8” with “3” and that gives you “24”. You now have the equation “16x + 24 = 48”.
The next step is to subtract “24” with “48”. This leaves you with “24”. Then you now have “16x = 24” as your new equation. The last step is to divide “16x” with “16”, this cancels it out with itself. Then you divide “24” with “16” and you get 1.5. So “X” equals 1.5 or you can convert it into a fraction witch gives you “3/4”.

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Complete Question:

There are 8 rows and 8 columns, or 64 squares on a chessboard.

Suppose you place 1 penny on Row 1 Column A,

2 pennies on Row 1 Column B,

4 pennies on Row 1 Column C, and so on …

Determine the number of pennies in Row 1

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Answer:

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Step-by-step explanation:

Given

$Rows = 8$

$Columns = 8$

Solving (a): Number of pennies in first row

The question is an illustration of geometric sequence which follows

$1,2,4....$

Where

$a =1$ --- The first term

Calculate the common ratio, r

$r = \frac{T_2}{T_1} = \frac{4}{2} = 2$

The number of pennies in the first row will be calculated using sum of n terms of a GP.

$S_n = \frac{a(r^n - 1)}{n - 1}$

Since, the first row has 8 columns, then

$n = 8$

Substitute 8 for n, 2 for r and 1 for a in $S_n = \frac{a(r^n - 1)}{r - 1}$

$S_8 = \frac{1 * (2^8 - 1)}{2 - 1}$

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$S_8 = \frac{1 * 255}{1}$

$S_8 = 255$

Solving (b): The entire board has 64 cells.

So:

$n = 64$

Substitute 64 for n, 2 for r and 1 for a in $S_n = \frac{a(r^n - 1)}{r - 1}$

$S_{64} = \frac{1 * (2^{64} - 1)}{2 -1}$

$S_{64} = \frac{(2^{64} - 1)}{1}$

$S_{64} = \frac{(18,446,744,073,709,551,616 - 1)}{1}$

$S_{64} = \frac{18,446,744,073,709,551,615}{1}$

$S_{64} = 18,446,744,073,709,551,615$

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