Find two consecutive whole numbers such that 4/7 of the larger exceeds 1/2 of the smaller by 5

The consecutive numbers are 62 and 63

Step-by-step explanation:

Let the larger number be represented by x and the smaller number by y,

Provided they are consecutive numbers;

--- Equation 1

From the question; we have that

--- Equation 2

Required

Find x and y

Multiply both sides of equation 2 by 14

---- Equation 3

Substitute y + 1 for x in equation 2

Open bracket

Collect like terms

So,

Hence, the consecutive numbers are 62 and 63

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2