Question

unit 6 quiz 1
problem 1:

1. story: lin bought 4 bags of apples. each bag had the same number of apples.

after eating 1 apple from each bag, she had 28 apples left. circle the tape diagram that
matches the story, you do not need to solve for the variable.
problem 2:
here is a tape diagram a student created.
a. write an equation that represents the tape diagram.
b. solve for the variable.
you must show your work to receive credit.
for problems #3 and #4, solve for the unknown value. you must show your work to receive credit.
problem 3:
3x + 7 = 67
problem 4:
10x - 7 = 28

Explanation:

Problem 1:

Let the number of apples in each bag be \(x\). Lin ate 1 apple from each of the 4 bags. So the number of apples left in each bag is \(x - 1\), and the total number of apples left is \(4(x - 1)\) which is equal to 28. So the correct tape - diagram is C.

Problem 2:

a.

The total length of the tape - diagram is \(4x+23\) and it is equal to \(17\) (assuming the other part of the tape - diagram). So the equation is \(4x+23 = 17\).

b.

Step1: Subtract 23 from both sides

$$
LATEXBLOCK0
$$

Step2: Divide both sides by 4

$$ x=\frac{-6}{4}=-\frac{3}{2}=-1.5 $$

Problem 3:

Step1: Subtract 7 from both sides

$$
LATEXBLOCK1
$$

Step2: Divide both sides by 3

$$ x=\frac{60}{3}=20 $$

Problem 4:

Step1: Add 7 to both sides

$$
LATEXBLOCK2
$$

Step2: Divide both sides by 10

$$ x=\frac{35}{10}=\frac{7}{2}=3.5 $$

Answer:

• Problem 1: C
• Problem 2a: \(4x + 23=17\)
• Problem 2b: \(x=-1.5\)
• Problem 3: \(x = 20\)
• Problem 4: \(x=3.5\)