linear equation word problem

Question

A store is having a sale on almonds and jelly beans.

For 6 pounds of almonds and 2 pounds of jelly beans, the total cost is $24

For 3 pounds of almonds and 5 pounds of jelly beans, the total cost is $21

Find the cost for each pound of almonds and each pound of jelly beans.

Answer 1

6a + 2j = 24

3a + 5j = 21

elimination method: -2 * EQ2 + EQ1

-8j = -18

j = -18/-8 = 9/4 = 2.25

2nd equation says a = (21 - 5J) / 3

= (21 - 45/4) / 3

= (84-45)/12

= 39/12

= 13/4

= 3.25

6(13/4) + 2(9/4) = 78/4 + 18/4 = 96/4 = 24

3(13/4) + 5(9/4) = 39/4 + 45/4 = 84/4 = 21

the almonds cost $3.25 per pound

the jelly beans cost $2.25 per pound

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And now I just noticed that the top equation can be divided by 2.

3a + j = 12

3a + 5j = 21

Subtracting EQ2 - EQ1 :

4j = 9

j = 9/4=2.25

3a + 9/4 = 12

12a + 9 = 36 <-- multiplies by 4

12a = 27

a = 27/12 = 9/4 = 2.25

Either way....