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3 years ago

13.) Springfield Elementary is putting on a school play

Mathematics

1 answer:

Oduvanchick [21]3 years ago

3 0

45 adult tickets and 80 children tickets were sold

Solution:

Let "a" be the number of adult tickets sold

Let "c" be the number of children tickets sold

Cost of 1 adult ticket = $ 6

Cost of 1 children ticket = $ 3.50

They sold a total of 125 tickets

Therefore,

a + c = 125

c = 125 - a --------- eqn 1

They made a total of $550. Therefore, frame a equation as:

number of adult tickets sold x Cost of 1 adult ticket + number of children tickets sold x Cost of 1 children ticket = 550

$a \times 6 + c \times 3.50 = 550\\$

6a + 3.50c = 550 ----------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

6a + 3.50(125 - a) = 550

6a + 437.5 - 3.50a = 550

2.5a = 112.5

Substitute a = 45 in eqn 1

c = 125 - 45

Thus 45 adult tickets and 80 children tickets were sold

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Solve each inequality, and then drag the correct solution graph to the inequality.

Nesterboy [21]

The correct solution graph to the inequalities are

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$1.6(x+8)\geq 38.4$ → B

(NOTE: The graphs are labelled A, B and C from left to right)

For the first inequality,

$4(9x-18)>3(8x+12)$

First, clear the brackets,

$36x-72>24x+36$

Then, collect like terms

$36x-24x>36+72\\12x >108$

Now divide both sides by 12

$\frac{12x}{12} > \frac{108}{12}$

∴ $x > 9$

For the second inequality

$-\frac{1}{3}(12x+6) \geq -2x +14$

First, clear the fraction by multiplying both sides by 3

$3 \times[-\frac{1}{3}(12x+6)] \geq3 \times( -2x +14)$

$-1(12x+6) \geq -6x +42$

Now, open the bracket

$-12x-6 \geq -6x +42$

Collect like terms

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$-48\geq 6x$

Divide both sides by 6

$\frac{-48}{6} \geq \frac{6x}{6}$

$-8\geq x$

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For the third inequality,

$1.6(x+8)\geq 38.4$

First, clear the brackets

$1.6x + 12.8\geq 38.4$

Collect likes terms

$1.6x \geq 38.4-12.8$

$1.6x \geq 25.6$

Divide both sides by 1.6

$\frac{1.6x}{1.6}\geq \frac{25.6}{1.6}$

∴ $x \geq 16$

Let the graphs be A, B and C from left to right

The first graph (A) shows $x\leq -8$ and this matches the 2nd inequality

The second graph (B) shows $x \geq 16$ and this matches the 3rd inequality

The third graph (C) shows $x > 9$ and this matches the 1st inequality

Hence, the correct solution graph to the inequalities are

$4(9x-18)>3(8x+12)$ → C

$-\frac{1}{3}(12x+6) \geq -2x +14$ → A

$1.6(x+8)\geq 38.4$ → B

Learn more here: brainly.com/question/17448505

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