ExplanationSince “the price of a phone call consists of a standard connection fee, which is a constant, plus a per-minute charge,” write a formula, using variables for the unknown information. Let c equal the connection fee and r equal the per-minute rate:

\(2.90 = c + r(10)\)

\(4.40 = c + r(16)\)

Now, either substitute and solve or stack and combine the equation. Note that there is one c in each equation, so subtracting is likely to be fastest:

\(4.40 = c + 16r\)

\(- (2.90 = c + 10r)\)

\(1.50 = 6r\)

\(r = 0.25\)

The calls cost 25 cents per minute. Note that most people will next plug r back into either equation to find c, but c isn’t necessary to solve!

A 10-minute call costs \(\$2.90\). That \(\$2.90\) already includes the basic connection fee (which is a constant) as well as the per-minute fee for 10 minutes. The problem asks how much a 13-minute call costs. Add the cost for another 3 minutes ($0.75) to the cost for a 10-minute call ($2.90): \(2.90 + 0.75 = \$3.65\).

In fact, both the 10-minute and 16-minute calls include the same connection fee (which is a constant), so a shortcut can be used to solve. The extra 6 minutes for the 16-minute call cost a total of $4.40 – $2.90 = $1.50. From there, calculate the cost per minute (1.5 ÷ 6 = 0.25) or notice that 13 minutes is halfway between 10 minutes and 16 minutes, so the cost for a 13-minute call must also be halfway between the cost for a 10-minute call and the cost for a 16-minute call. Add half of $1.50, or $0.75, to $2.90 to get $3.65.

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Sandy

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