Question

Model each problem as an equation, and then match to its solution.

Answer 1

Answer:

Part 1) The larger integer is 11

Part 2) The denominator is 5

Part 3) The positive integer is 4

The graph in the attached figure

Step-by-step explanation:

Part 1)

Let

x----> the smaller positive integer

y-----> the larger positive integer

we know that

$x^{2} +y^{2} =185$ -----> equation A

$x=y-3$ -----> equation B

substitute equation B in equation A and solve for y

$(y-3)^{2} +y^{2} =185\\ \\y^{2} -6y+9+y^{2}=185\\ \\2y^{2}-6y-176=0$

using a graphing calculator-----> solve the quadratic equation

The solution is y=11

$x=11-3=8$

Part 2)

Let

x----> the numerator of the fraction

y-----> the denominator of the fraction

we know that

$x=2y+1$ ----> equation A

$\frac{x+4}{y+4}=\frac{5}{3}$ ----> equation B

substitute equation A in equation B and solve for y

$\frac{2y+1+4}{y+4}=\frac{5}{3}$

$\frac{2y+5}{y+4}=\frac{5}{3}\\ \\6y+15=5y+20\\ \\6y-5y=20-15\\ \\y=5$

$x=2(5)+1=11$

Part 3)

Let

x----> the positive integer

we know that

$x-\frac{1}{x}=\frac{15}{4}$

solve for x

$x-\frac{1}{x}=\frac{15}{4}\\ \\4x^{2}-4=15x\\ \\4x^{2}-15x-4=0$

using a graphing calculator-----> solve the quadratic equation

The solution is x=4