Question

The math team wraps gifts as a way to raise money for traveling to competitions. They offer two choices: a plain wrapping or a decorative wrapping with bows. The table represents the money raised over a busy shopping weekend.

A 3-column table titled Gift-Wrapping Fundraiser has 3 rows. The first column is labeled Plain Gifts Wrapped with entries 10, 25, 16. The second column is labeled Decorative Gifts Wrapped with entries 9, 12, 12. The third column is labeled Total Raised in dollars with entries 47, 86, 68.
Which statement describes the amounts the team charged for wrapping gifts?

1. Step-by-step explanation:
We will assume that the first two columns are the numbers sold for Plain Wrapping and Decorative Wrapping.  The third colum does not equal the sum of the first two, so we’ll assume it is the total paid for both options.  Let set the price of Plain Wrapping to x and the Decorative Wrapping to y.  The number of gift wrappings times the cost per warpping is the product of x or y timers the number wrapped as shown in columns 1 and 2.
Take the first row and set it as an equation:
10x+9y = 47   [10 Plain Wraps and 9 Decorative Wraps bring a total of $47] Do the same for the second and third rows: 25x + 12y = 86, and 16x +12y = 68 =========== We can take any equation and rearrange it to isolate one of the 2 variables, x or y. I’ll pick 10x = 47-9y and isolate x: 10x = 47-9y x = (47-9y)/10 ——————- Now use this definition of x in another equation. I’ll use 25x + 12y = 86. 25x + 12y = 86 25(47-9y)/10 + 12y = 86 [since x = (47-9y)/10 from above] 117.5 – 22.5y + 12y = 86 -10.5y = -31.5 y = 3 [the price for decorative wrapping is$3]
If y = 3, then we can use this in any of the equations to find x:
x = (47-9y)/10
x = (47-9(3))/10     [Use y = 3]
x = (47-27)/10
x = 2                              [The price for plain wrapping is $3] ====================== Check to see if these values will expalin the total value of the three rows of numbers: CHECK: ______UNITS____$2 each          $3 each PlainW DecG Total PlainW ($)      DecG ($) Total ($)
x           y                          x                       y
10         9        $47$20                    $27$ 47         OK
25        12       $86$50                    $36$ 86         OK
16        12       $68$32                    $36$ 68         OK
The values work.  Merry Christmas.

2. The team charged $2 to wrap a gift with no bow and$3 to wrap a gift with a bow.