ExplanationAssign one variable to the pencils and another variable to the pens:

Number of pencils = x

Number of pens = y

\(x + y = 10\)

\(70y + 40x = 520\)

The question asks for the number of pencils, x, so isolate y in the first equation and substitute into the second:

\(y = 10 - x\)

\(70(10 - x) + 40x = 520\)

\(700 - 70x + 40x = 520\)

\(700 - 30x = 520\)

\(180 = 30x\)

\(x = 6\)

Alternatively, test the answer choices. Starting with the middle choice, if Iris bought 8 pencils and therefore 2 pens, she spent (8 × 40) + (2 × 70) = 320 + 140 = 460. That’s 60 cents too little, so Iris must have bought fewer pencils and more pens. Try 6 pencils and 4 pens: (6 × 40) + (4 × 70) = 240 + 280 = 520. (You might also have noticed that every time Iris swaps a pencil for a pen, she spends an extra 30 cents.)

Hence option B is correct!
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Sandy

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