2/5/2021 Sophia :: Welcome
Score 17/20
You passed this Milestone
17 questions were answered correctly.
UNIT 2 — MILESTONE 2
3 questions were answered incorrectly.
1
Jacob opened a money-market account. In the first month, he made an initial deposit of $500, and he plans to contribute an additional $75 every month. The account does
not pay any interest.
After how many months will he have a total of $1,475?
15 months
13 months
12 months
14 months
RATIONALE
The amount in Jacob's deposit account can be modeled using the formula for an arithmetic sequence. The term a subscript n is the value after
n months, a subscript 1 is the initial balance, d is the common difference (or steady monthly deposits), and n is the number of months. Use the
information provided to find each value.
The initial deposit, , is $500. Jacob deposits $75 each month, which is the difference, d. We want to know how many months, n, it will take
for the balance to reach $1475, which is the value for . Next, substitute each value in for , d, and .
Once each known value is substituted, we can solve for n. First, distribute 75 into (n – 1).
75(n – 1) is equivalent to 75n – 75. Next, combine like terms on the right side.
500 minus 75 is equal to 425. Subtract this value from both sides to isolate the n term.
1475 minus 425 equals 1050. Finally divide both sides by 75.
1050 divided by 75 is equal to 14. It will take 14 months for the balance to reach $1,475.
CONCEPT
Introduction to Arithmetic Sequences
2
Christine paid $633.68 (including sales tax) for a handbag. The sales tax in her state is 6.5%.
What was the price of the handbag before the sales tax was added?
$595.00
$587.50
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$590.00
$592.50
RATIONALE
To calculate the price of an item with tax included, multiply the original price of the item by (1 + r), where r is the percent tax
expressed as a decimal. The price of the handbag with tax included is $633.68 and the percent tax, r, is 6.5%, or 0.065 when
written as a decimal. Substitute these values in the equation and solve for the original price.
Once the known values are substituted into the formula, evaluate the parentheses by adding 1 and 0.065.
1 plus 0.065 equals 1.065. Next, undo the multiplication on the right side by dividing both sides by 1.065.
$633.68 divided by 1.065 is $595.00. The price of the handbag without sales tax is $595.00.
CONCEPT
Solving Problems involving Percents
3
Suppose 4y – 1 = 15 and y = 5x – 3.
Which of the following equations is equivalent to 4y – 1 = 15, but written only in terms of x?
5x – 12 = 16
20x – 12 = 14
5x – 12 = 14
20x – 12 = 16
RATIONALE
To find an equivalent equation written in terms of x we can use the second equation y = 5x – 3. This equation indicates that y is equivalent to 5x – 3
so we can substitute (5x – 3) in for y in the first equation 4y – 1 = 15.
Now we have an equation in terms of x. To simplify it, first apply the Distributive Property and multiply 4 by the terms in the parentheses.
4 times 5x equals 20x, and 4 times -3 equals -12. Next, eliminate -1 from the left side of the equation by adding 1 to both sides.
15 plus 1 equals 16. This equation is equivalent to the original equation, but is written in terms of x.
CONCEPT
Substitution in multi-step linear equations
4
The value V (in dollars) of a milling machine depends on the number of hours x it is operated as given by the formula V = 750,000 – 120x. After one year, the value of the
milling machine is between $450,000 and $480,000.
Which range for the hours the machine is operated does this correspond to?
2750 ≤ x ≤ 3000
2400 ≤ x ≤ 2650
2250 ≤ x ≤ 2500
2500 ≤ x ≤ 2750
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Score 17/20
You passed this Milestone
17 questions were answered correctly.
UNIT 2 — MILESTONE 2
3 questions were answered incorrectly.
1
Jacob opened a money-market account. In the first month, he made an initial deposit of $500, and he plans to contribute an additional $75 every month. The account does
not pay any interest.
After how many months will he have a total of $1,475?
15 months
13 months
12 months
14 months
RATIONALE
The amount in Jacob's deposit account can be modeled using the formula for an arithmetic sequence. The term a subscript n is the value after
n months, a subscript 1 is the initial balance, d is the common difference (or steady monthly deposits), and n is the number of months. Use the
information provided to find each value.
The initial deposit, , is $500. Jacob deposits $75 each month, which is the difference, d. We want to know how many months, n, it will take
for the balance to reach $1475, which is the value for . Next, substitute each value in for , d, and .
Once each known value is substituted, we can solve for n. First, distribute 75 into (n – 1).
75(n – 1) is equivalent to 75n – 75. Next, combine like terms on the right side.
500 minus 75 is equal to 425. Subtract this value from both sides to isolate the n term.
1475 minus 425 equals 1050. Finally divide both sides by 75.
1050 divided by 75 is equal to 14. It will take 14 months for the balance to reach $1,475.
CONCEPT
Introduction to Arithmetic Sequences
2
Christine paid $633.68 (including sales tax) for a handbag. The sales tax in her state is 6.5%.
What was the price of the handbag before the sales tax was added?
$595.00
$587.50
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7603243 1/12
, 2/5/2021 Sophia :: Welcome
$590.00
$592.50
RATIONALE
To calculate the price of an item with tax included, multiply the original price of the item by (1 + r), where r is the percent tax
expressed as a decimal. The price of the handbag with tax included is $633.68 and the percent tax, r, is 6.5%, or 0.065 when
written as a decimal. Substitute these values in the equation and solve for the original price.
Once the known values are substituted into the formula, evaluate the parentheses by adding 1 and 0.065.
1 plus 0.065 equals 1.065. Next, undo the multiplication on the right side by dividing both sides by 1.065.
$633.68 divided by 1.065 is $595.00. The price of the handbag without sales tax is $595.00.
CONCEPT
Solving Problems involving Percents
3
Suppose 4y – 1 = 15 and y = 5x – 3.
Which of the following equations is equivalent to 4y – 1 = 15, but written only in terms of x?
5x – 12 = 16
20x – 12 = 14
5x – 12 = 14
20x – 12 = 16
RATIONALE
To find an equivalent equation written in terms of x we can use the second equation y = 5x – 3. This equation indicates that y is equivalent to 5x – 3
so we can substitute (5x – 3) in for y in the first equation 4y – 1 = 15.
Now we have an equation in terms of x. To simplify it, first apply the Distributive Property and multiply 4 by the terms in the parentheses.
4 times 5x equals 20x, and 4 times -3 equals -12. Next, eliminate -1 from the left side of the equation by adding 1 to both sides.
15 plus 1 equals 16. This equation is equivalent to the original equation, but is written in terms of x.
CONCEPT
Substitution in multi-step linear equations
4
The value V (in dollars) of a milling machine depends on the number of hours x it is operated as given by the formula V = 750,000 – 120x. After one year, the value of the
milling machine is between $450,000 and $480,000.
Which range for the hours the machine is operated does this correspond to?
2750 ≤ x ≤ 3000
2400 ≤ x ≤ 2650
2250 ≤ x ≤ 2500
2500 ≤ x ≤ 2750
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7603243 2/12
