for delivering packages, the cross town courier

Question

for delivering packages, the cross town courier service charges a set amount for the first 50g abd a fixed rate fir each additional 10g. the charge for a 210g package is 5.60. the charge for a 330g package is 7.40 what is the cost for each additional 10 grams

Answer 1

Hi Rick,

 

Let's begin by assigning letters to represent our two unknowns:

    x = set amount for first 50 grams

    y = fixed rate for each additional 10 grams

 

Next, let's write two equations which we can use to solve for our two unknowns:

    Equation #1 (total charge for 210 gram package):

        x + [(210 - 50)/10]y = 5.6

        x + (160/10)y = 5.6

        x + 1.6y = 5.6 (Equation #1) 

    Equation #2 (total charge for 330 gram package):

        x + [(330 - 50)/10]y = 7.4

        x + (280/10)y = 7.4

        x + 2.8y = 7.4 (Equation #2)

 

Next, let's subtract Equation #1 from Equation #2 to eliminate x and solve for y:

    x + 2.8y = 7.4   [Equation #2]

 - (x + 1.6y = 5.6)  [Equation #1]

 ---------------------

          1.2y = 1.8

               y = 1.8/1.2

               y = 3/2

               y = 1.5

    $1.50 (fixed rate for each additional 10 grams)

 

Finally, let's verify our answer for y by plugging it back into each equation and see if we get the SAME answer for x, i.e. the SAME set amount for the first 50 grams:

    x + 1.6y = 5.6 (Equation # 1)

        x + 1.6(1.5) = 5.6 (plug-in answer for y)

        x + 2.4 = 5.6

        x = 5.6 - 2.4

        x = 3.2

    x + 2.8y = 7.4 (Equation #2)

        x + 2.8(1.5) = 7.4

        x + 4.2 = 7.4

        x = 7.4 - 4.2

        x = 3.2

    $3.20 = $3.20

    (SAME fixed set amount for first 50 grams)

 

Since our plugged-in answer for y gives the SAME answer for x (SAME set amount for first 50 grams) in both equations, we are confident that our answer for y (fixed rate for each additional 10 grams) is correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.