Vintage US Postcards

How would I solve these two word problems?

A shopper pays $20.75 for four pounds of a nut mixture consisting of almonds and pecans. If almonds cost $3.50 per pound and pecans cost $6.00 per pound, how much of each were purchased?

Solve as a system of equations where x = weight of Almonds and y = weight of Pecans
The second equation is weight multiplied by price to give the total price of the mixed nuts.

x + y = 4
3.5x + 6y = 20.75
-------------------------

-6(x + y = 4) .....multiply by (-6) so that you can add the 2 equations isolating x

-6x - 6y = -24
3.5x + 6y = 20.75
-----------------------
-2.5x + 0y = -3.25
-2.5x/-25 = -3.25/-2.5 ... divide both sides by -2.5 to isolate x
x = 1.3

through substitution now find y
1.3 + y = 4
y = 4 - 1.3
y = 2.7

check your answer by inserting both values into the 2nd equation

3.5(1.3) + 6(2.7) = 20.75
4.55 + 16.20 = 20.75 check ... 1.3lbs Almonds 2.7lbs of Pecans

=============

2nd problem is the same type as the first

x = # of postcards y = # of letters

x + y = 56
.27x + .42y = 21.72
----------------------------

100(0.27x + 0.42y = 21.72) .... do this to eliminate the fractions.

x + y = 56
27x + 42y = 2172
---------------------------

-27( x + y = 56) .... multiply the equation by (-27) so that you can add the 2 equations isolating y to find the number of letters

-27x - 27y = -1512
27x + 42y = 2172
------------------------------
0x + 15y = 660

15y/15 = 660/15 ...divide both sides by 15 to isolate y
y = 44

through substitution now find x

x + 44 = 56
x = 56 - 44
x = 12

check your answer by inserting both values into the 2nd equation

.27(12) + .42(44) = 21.72
3.24 + 18.48 = 21.72 ......... check ... 12 postcards .. 44 letters

edited for clarity

pc1348 postcard New Jersey SEVEN Mixture $9.99 Time Remaining: 2d 15h 44m Buy It Now for only: $9.99

pc2736 postcard New Jersey Mixture EIGHT $8.00 Time Remaining: 3d 8h 24m Buy It Now for only: $8.00

pc2744 postcard New Jersey Mixture EIGHT $8.00 Time Remaining: 3d 8h 25m Buy It Now for only: $8.00

pc4765 postcard Missouri Mixture $6.00 Time Remaining: 3d 11h 27m Buy It Now for only: $6.00

pc4313 postcard California Mixture TEN Different $9.99 Time Remaining: 4d 13h 21m Buy It Now for only: $9.99

1940s Brindleys Mixture Tobacco Faber Pittsburgh PA MB $3.49 Time Remaining: 6d 16h 41m Buy It Now for only: $3.49

pc2545 postcard Chicago Illinois Mixture TEN $9.99 Time Remaining: 6d 17h 15m Buy It Now for only: $9.99

pc2571 postcard Chicago Illinois Mixture TEN Not used $9.99 Time Remaining: 6d 17h 15m Buy It Now for only: $9.99

pc3446 postcard New Jersey Mixture EIGHT $8.00 Time Remaining: 7d 9h 3m Buy It Now for only: $8.00

pc3465 postcard New Jersey Mixture TEN $5.00 Time Remaining: 7d 9h 3m Buy It Now for only: $5.00

pc3481 postcard New Jersey Mixture EIGHT $8.00 Time Remaining: 7d 9h 4m Buy It Now for only: $8.00

pc4381 postcard California Mixture SIX Different $4.00 Time Remaining: 7d 9h 9m Buy It Now for only: $4.00

pc823 postcard Sacramento California Mixture SIX $9.99 Time Remaining: 9d 13h 18m Buy It Now for only: $9.99

pc3961 postcard Ohio Mixture TEN Different $6.00 Time Remaining: 12d 10h 35m Buy It Now for only: $6.00

pc4024 postcard California Mixture FIVE Different $4.00 Time Remaining: 12d 11h Buy It Now for only: $4.00

pc567 postcard Switzerland Mixture TWELVE $9.99 Time Remaining: 16d 13h 18m Buy It Now for only: $9.99

pc2738 postcard Utah State Mixture EIGHT 1 used 1947 7 not used $8.00 Time Remaining: 16d 17h 6m Buy It Now for only: $8.00

pc2741 postcard Utah State Mixture EIGHT All MOBSC Not used $8.00 Time Remaining: 16d 17h 6m Buy It Now for only: $8.00

pc1055 postcard Arkansas Mixture EIGHT $8.00 Time Remaining: 20d 5h 5m Buy It Now for only: $8.00

pc5887 postcard Indianapolis Indiana Mixture ELEVEN $6.00 Time Remaining: 20d 13h 11m Buy It Now for only: $6.00

pc5573 postcard New Hampshire TWENTY TWO Mixture $9.99 Time Remaining: 21d 4h 27m Buy It Now for only: $9.99

pc5575 postcard New Jersey FOURTEEN Mixture $5.00 Time Remaining: 21d 4h 27m Buy It Now for only: $5.00

pc5576 postcard New York TWENTY FOUR Mixture $9.99 Time Remaining: 21d 4h 28m Buy It Now for only: $9.99

pc4105 postcard Miami Beach FL FOUR Mixture $4.00 Time Remaining: 21d 11h 41m Buy It Now for only: $4.00

pc5170 postcard EIGHT Ohio Mixture $8.00 Time Remaining: 23d 11h 28m Buy It Now for only: $8.00

pc259 postcard California Mission Mixture NINE All MOBSC $9.99 Time Remaining: 25d 7h 47m Buy It Now for only: $9.99

pc7966 postcard Sail Boats Mixture All Mobsc NINE $9.00 Time Remaining: 25d 10h 46m Buy It Now for only: $9.00

pc2719 postcard Christmas Mixture 1920 FIVE $4.00 Time Remaining: 26d 5h 59m Buy It Now for only: $4.00

DERBYS CROUP AND COUGH MIXTURE EATON RAPIDS MI DERBY MEDICINE CO $29.99 Time Remaining: 26d 11h 29m Buy It Now for only: $29.99

pc3631 postcard Illinois Mixture TWELVE $4.00 Time Remaining: 27d 3h 48m Buy It Now for only: $4.00

pc3632 postcard Indiana Mixture FIVE $4.00 Time Remaining: 27d 3h 48m Buy It Now for only: $4.00

pc3640 postcard Massachusetts Mixture NINE $4.00 Time Remaining: 27d 3h 49m Buy It Now for only: $4.00

pc3643 postcard Michigan Mixture NINE $4.00 Time Remaining: 27d 3h 49m Buy It Now for only: $4.00

pc3656 postcard Ohio Mixture FOURTEEN $6.00 Time Remaining: 27d 3h 51m Buy It Now for only: $6.00

pc3814 Postcards California SEVEN postcard Mixture $4.00 Time Remaining: 27d 4h 4m Buy It Now for only: $4.00

pc3816 Postcards Chicago Illinois THREE Mixture $4.00 Time Remaining: 27d 4h 4m Buy It Now for only: $4.00

pc3871 Postcards New York Mixture SIX $4.00 Time Remaining: 27d 4h 6m Buy It Now for only: $4.00

pc5686 postcard Springfield Illinois Mixture EIGHT Mint $8.00 Time Remaining: 27d 16h 32m Buy It Now for only: $8.00

pc3768 postcard Kansas Mixture EIGHT Postcards $6.00 Time Remaining: 29d 6h 40m Buy It Now for only: $6.00

pc4064 postcard New Hampshire Mixture FIVE $4.00 Time Remaining: 29d 9h 23m Buy It Now for only: $4.00