Question

quiz 1 solving equations

1. a gardener is buying bags of soil for a landscaping project. each bag of soil costs $5.50. the gardener receives an eight-dollar discount at the register. if the total final cost is $19.50, write an equation to determine the number of bags of soil, x, the gardener purchased.
2. rewrite $a = \frac{bh}{2}$ in terms of $h$.
3. solve for x. $\frac{x}{4}+3 = 7$
4. solve for x. $3(x - 2)+12 = 3x + 6$
5. the problem was solved incorrectly. circle the error, and solve it correctly.

$5x + 15+4x = 6x - 3(x + 9)$
students work:
$5x + 15+4x = 6x - 3(x + 9)$
$9x + 15 = 6x - 3x + 27$
$9x + 15 = 3x + 27$
$-6x -6x$
$3x + 15 = 27$
$3x = 27 - 15$
$3x = 13$
$\frac{3x}{3}=\frac{13}{3}$
$x = 3$

1. in which step did we make a mistake?

rewrite the formula for the area of a trapezoid in terms of $b_1$.
$a = \frac{1}{2}h(b_1 + b_2)$

1. $2a = h(b_1 + b_2)$
2. $2ah = b_1 + b_2$
3. $2ah - b_2 = b_1$
4. solve for x. $|5x + 10|+25 = 16$
5. solve for x. $|5x + 10|+1 = 16$

Explanation:

1)

Step1: Define cost equation

$5.50x - 8 = 19.50$

Step2: Isolate variable term

$5.50x = 19.50 + 8$
$5.50x = 27.50$

Step3: Solve for x

$x = \frac{27.50}{5.50}$

Step1: Eliminate denominator

$2A = bh$

Step2: Isolate h

$h = \frac{2A}{b}$

Step1: Isolate fraction term

$\frac{x}{4} = 7 - 3$
$\frac{x}{4} = 4$

Step2: Solve for x

$x = 4 \times 4$

Answer:

$x = 5$

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2)