Question

Susan, wade, and Bethany sold greeting cards to raise money for their Christian schools computer lab. they sold a total of 71 boxes. wade sold one less than twice as many Susan, and Bethany sold three times as many as Susan. how many boxes did each student sell?

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Let:}}}}$

• $\rm{boxes\: sold\:by\:Susan\:be\:x}$
• $\rm{boxes\: sold\:by\:wade\:be\:2x-1}$
• $\rm{boxes\: sold\:by\: Bethany\:be\:3x}$

$\large{\underline{\red{\rm{To\:Find:}}}}$

• $\rm{How\:many\:boxes\:did\:sell\:each\: students}$

$\large{\underline{\red{\rm{Given:}}}}$

• they sold a total of 71 boxes. wade sold one less than twice as many Susan, and Bethany sold three times as many as Susan.

$\small{\underline{\green{\rm{According\: to\: question:}}}}$

• $\rm\green{sold\:the\:boxes\:by\: students=Total\: Boxes}$

$\rm{\implies 2x-1+3x+x=71}$

$\rm{\implies 2x+3x+x=71+1}$

$\rm{\implies \cancel{6}x=\cancel{72}}$

$\rm\purple{\implies x=12}$

Hence,

$\rm{\implies boxes\: sold\:by\:Susan=12}$

$\rm{\implies boxes\: sold\:by\:wade=2x-1=2*12-1=23}$

$\rm{\implies boxes\: sold\:by\:Bathany=3x=3*12=36}$

$\huge{\underline{\purple{\rm{Verification:}}}}$

$\rm{\implies (2*12-1)+3*12+12=71}$

$\rm{\implies 23+36+12=71}$

$\rm{\implies 71=71}$

$\large\rm\purple{\implies Hence,\:LHS=RHS\: Proved}$

Answer 2

Answer:

Susan = 12 boxes

Wade = 23 boxes

Bethany = 36 boxes

Step-by-step explanation:

Given:

Total number of boxes = 71

Let the boxes sold by Susan be X

According to the question,

Boxes sold by Wade = (2X-1)

Boxes sold by Antony =3X

So, the sum of boxes of Susan, wade and Antony will be equal to 71

Substituting the values, we get:

(X+2X-1+3X)=71

(3X-1+3X)=71

(6X-1)=71

6X = 71+1

6X = 72

$x = \frac{72}{6}$

$x = 12$

The boxes sold by Susan = 12

Boxes sold by Wade = (2×12)-1 = 24 - 1 = 23

Boxes sold by Bethany = (3×12) = 36 boxes

Susan sold 12 boxes, wade sold 23 boxes and Bethany sold 36 boxes

Verification

The sum of everyone's boxes should be equal to

71,

12 + 23 + 36 = 71

= 35 + 36 = 71

= 71 = 71

Hence verified