Question

fa2 quiz 1.1 review #2
period : __________

1. your friend goes to solve the following problem and shows you their work. is this work correct? if so, write correct. if not, circle the mistake, and then solve the problem correctly starting from their mistake.

step 1 : − 1.5 + k = 8.2

step 2 : k = 8.2 + (− 1.5)

step 3 : k = 6.7

1. you work at home depot, and have been noticing that the price of some items have been changing weekly. you see that the new samsung smart refrigerator is listed at $2350 this week. you have been told this price is 1.25 times more than it was last week. setup and solve an equation to show what the price of the refrigerator was last week.

1. your most recent paycheck just hit your bank account, so you decide to go to target and treat yourself. while at target, you spent $63 on a new lego set, 2 new books, 3 alanis, and a bag of honey bbq fritos. after all was said and done, you still had $59 from your paycheck. setup and solve an equation to show how much money you originally had from your paycheck.

Explanation:

Question 9

Step1: Analyze the equation solving

The original equation is $-1.5 + k = 8.2$. To solve for $k$, we should add $1.5$ to both sides (or add the opposite of $-1.5$, which is $1.5$). In Step 2, the friend wrote $k = 8.2+(- 1.5)$ which is incorrect. The correct step should be $k=8.2 + 1.5$ (because to isolate $k$, we add $1.5$ to both sides: $-1.5 + k+1.5=8.2 + 1.5$).

Step2: Correct the mistake and solve

Starting from the mistake in Step 2, the correct equation is $k = 8.2+1.5$.
Calculating the right - hand side: $8.2 + 1.5=9.7$.

Step1: Define the variable and set up the equation

Let $x$ be the price of the refrigerator last week. We know that this week's price ($2350$) is $1.25$ times last week's price. So the equation is $1.25x=2350$.

Step2: Solve the equation for $x$

To solve for $x$, we divide both sides of the equation by $1.25$. So $x=\frac{2350}{1.25}$.
Calculating $\frac{2350}{1.25}$, we can multiply the numerator and denominator by 4 to get rid of the decimal in the denominator: $\frac{2350\times4}{1.25\times4}=\frac{9400}{5} = 1880$.

Step1: Define the variable and set up the equation

Let $y$ be the original amount of money from the paycheck. The amount spent is $\$63$ and the amount left is $\$59$. So the equation is $y-63 = 59$.

Step2: Solve the equation for $y$

To solve for $y$, we add $63$ to both sides of the equation. So $y=59 + 63$.
Calculating $59+63 = 122$.

Answer:

The work is incorrect. The mistake is in Step 2 (the incorrect expression is $k = 8.2+(-1.5)$). The correct solution is $k = 9.7$.

Question 10