Algebra I, Module 5, Lesson 7—Formulating Systems of Equations

Additional Problems with Solutions

Problem 1

The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics. The difference in price between the system at Extreme Electronics and Ultra Electronics is $175. Which system of linear equations can be used to determine the price of the system at each store?

A	2e – u = 220 e – u = -175	C	2e – 2u = 440 e – u = -175
B	2e – u = 220 e + u = 175	D	e – 2u = -220 e – u = 175

Equation 1

The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics.

Equation 2

The difference in price between the system at Extreme Electronics and Ultra Electronics is $175.

Equation 1. Translate each word or phrase.

The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics.

The price, e	Interactive popup. Assistance may be required. Check Your Answer e
is	Interactive popup. Assistance may be required. Check Your Answer =
220	Interactive popup. Assistance may be required. Check Your Answer 220
less than	Interactive popup. Assistance may be required. Check Your Answer –. Remember, when dealing with less than the order is reversed.
twice	Interactive popup. Assistance may be required. Check Your Answer Two times
the price u	Interactive popup. Assistance may be required. Check Your Answer u
Put your answers together to write an equation	Interactive popup. Assistance may be required. Check Your Answer e = 2u – 220

You may have thought the equation should be e = 220 – 2u but the word less than changed the order.

Be careful of the phrases less than, younger than, subtracted from, and fewer than.

Look at the answers again.

A	2e – u = 220 e – u = –175	C	2e – 2u = 440 e – u = –175
B	2e – u = 220 e + u = 175	D	e – 2u = –220 e – u = 175

Oh no! There is no answer choice e = 2u – 220. Did we do something wrong?

No, the writers of this question are being mean. They rearranged the equation.

No worries. We’re not going to let them get us down.

Translate each word or phrase.

The difference in price between the system at Extreme Electronics and Ultra Electronics is $175.

difference	Interactive popup. Assistance may be required. Check Your Answer –. Keep reading but we're going to subtract something.
Extreme Electronics	Interactive popup. Assistance may be required. Check Your Answer e    We know this from the last sentence/equation.
Ultra Electronics	Interactive popup. Assistance may be required. Check Your Answer u   We know this from the last sentence/equation.
is	Interactive popup. Assistance may be required. Check Your Answer =
175	Interactive popup. Assistance may be required. Check Your Answer 175
Put your answers together to write an equation	Interactive popup. Assistance may be required. Check Your Answer e – u = 175

Yes! Only one answer choice has the equation e – u = 175. D is the correct answer.

A	2e – u = 220 e – u = –175	C	2e – 2u = 440 e – u = –175
B	2e – u = 220 e + u = 175	D	e – 2u = –220 e – u = 175

You will want to know why the other equation is also correct. If you got the equation e = 2u – 220 you can change it by subtracting. If you subtract 2u from both sides of the equal sign you get:

        e = 2u – 220
-2u         -2u
e – 2u = -220

Problem 2

A school district held a meeting for all its physical education teachers. The number of women attending was 5 more than twice the number of men attending. A total of 53 teachers attended the meeting. Which system of equations could be used to find w, the number of women, and m, the number of men, at this meeting?

A	m = 2w + 5 w + m = 53	C	w = m + 5 w + m = 53
B	2w + m = 5 w + m = 53	D	w = 2m + 5 w + m = 53

You need to break down the information.

Equation 1 comes from:

The number of women attending was 5 more than twice the number of men attending.

Equation 2 comes from:

A total of 53 teachers attended the meeting.

Translate Equation 2 first. A total of 53 teachers doesn’t say a lot. But the previous sentence talked about male and female teachers. So you have to realize the sentence is telling you the total of male and female teacher is 53.

What equation would you write to translate the total of male and female teacher is 53.

Copy the phrase, A total of 53 teachers, into your notes, and translate to a mathematical equation.

Click the link below to see the answer.

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Check Your Answer

w + m = 53

Here are the answer choices again.

A	m = 2w + 5 w + m = 53	C	w = m + 5 w + m = 53
B	2w + m = 5 w + m = 53	D	w = 2m + 5 w + m = 53

Which answer choices can you eliminate?

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Check Your Answer

None, that equation didn't help at all.

Now you need to translate: The number of women attending was 5 more than twice the number of men attending.

In your notes, copy the words and phrases and translate them to math symbols. To check your work, highlight the boxes below.

Number of women	Interactive popup. Assistance may be required. Check Your Answer w
Was	Interactive popup. Assistance may be required. Check Your Answer =
5	Interactive popup. Assistance may be required. Check Your Answer 5
More than	Interactive popup. Assistance may be required. Check Your Answer +  If it were "is more than" that would be >.
Twice	Interactive popup. Assistance may be required. Check Your Answer two times
Number of men	Interactive popup. Assistance may be required. Check Your Answer m
Put your answers together to write an equation	Interactive popup. Assistance may be required. Check Your Answer w = 5 + 2m

No answer choices are exactly what we wrote above but I hope you know that you can turn around addition (commutative property: 2 + 5 = 5 + 2).

D is the correct answer choice.

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