Question

Match each word problem to the equation that models it.

Answer 1

see attached

Explanation:

You want to match the given word problem with a suitable equation for solving it.

1. Sum of Squares

The variable x is assigned to the larger of two numbers that differ by 2. That makes the smaller one (x -2). The sum of their squares is ...

x² + (x -2)² = 394

Simplifying, we get ...

x² +x² -4x +4 = 394

2x² -4x -390 = 0 . . . . . . . matches the first equation

2. Fraction

The numerator of the fraction is 5 more than its denominator, x, so will be (x +5). Adding 3 to numerator and denominator, we get ...

`((x+5)+3)/((x)+3)=(4)/(3)\\\\3(x+8)=4(x+3)\\\\\boxed{3x+24=4x+12}\qquad\textsf{matches the third equation}`

3. Reciprocal

The sum of x and its inverse is 4/3, so we have ...

x + 1/x = 4/3

Multiplying by 3x gives ...

3x² +3 = 4x

3x² -4x +3 = 0 . . . . . . . . . matches the second equation

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