s + t = 10
40 s + 20t = 340
To solve for s, use substitution. First, manipulate the first equation to express
t in terms of s: t = 10 – s. Next, substitute that expression for t in the second
equation: 40s + 20(10 – s) = 340. Solve for s:
40 s + 20(10 – s) = 340
40 s + 200 – 20s = 340
20 s = 14 0
s = 7- A Let c = the price of each computer and m = the price of each monitor.
The manufacturer thus paid a total of $3c for the computers and $5m for the
monitors. The sum of these values equals $4,000: 3c + 5m = 4,000. The other
algebraic relationship you can create from the information is c = 5m. There are
now two equations:
3 c + 5m = 4,000
c = 5m
To solve for m, substitute 5m in for c in the first equation: 3(5m) + 5m = 4,000.
Distribute and combine like terms: 20m = 4,000. Solve for m: m = 200. - D The question asks you to determine the amount paid per friend. This can
be expressed as the following ratio: total bill/number of people paying. The
numerator of this ratio will be 800. The denominator will be the total number
of friends splitting the bill after x do not pay. If there were 10 friends originally,
and x do not pay, the number of people paying is 10 – x. Thus the ratio will
be 10 –^800 x. - D Let b = Bob’s current age and j = Jack’s current age. You are asked to solve
for b + 5. Use the assigned variables to construct algebraic relationships. The
first sentence provides a relationship between Bob’s current age and Jack’s
current age: b = j + 10. The second sentence provides a relationship between
their ages in 2 years: b + 2 = 2(j + 2). Use substitution to solve for b:
Step 1: Manipulate the first equation to write j in terms of b: b – 10 = j
Step 2: Substitute b – 10 for j in the second equation:
b + 2 = 2(b – 10 + 2)
b + 2 = 2(b – 8)
b + 2 = 2b – 16
18 = b
In 5 years, Bob will be 23.- D Since you are asked to solve for the length of the call, you should assign a
variable: l = length of the call. The total charge of $5.75 consists of two parts:
the charge for the first minute and the charge for all subsequent minutes. The
CHAPTER 12 ■ FROM WORDS TO ALGEBRA 32304-GRE-Test-2018_313-462.indd 323 12/05/17 12:03 pm