At the store, 5 oranges and 14 bananas cost $6.60, whereas 8 oranges and 9 bananas costs $7.21. Determine the cost of each orange and each banana.

Question

 grade 10 math

Answer 1

Each of the two situations leads to an equation.

x = oranges

y = bananas

5x + 14 y = 6.60

8x +9y = 7.21

 

Solve by elimination.  Multiply the first equation by 8 and the second one by 5.

40x + 112y = 52.80

40x +   45y = 36.05   Subtract

             67y = 16.75

y = 0.25 per banana

 

Substitute for y in either equation and solve for x.

5x + (14)(0.25) = 6.60

5x = 6.60 - 3.50

5x = 3.10

x = 0.62 per orange

 

Check:

(5)(0.62) + (14)(0.25) =? 6.60

3.10 + 3.50 =? 6.60

6.60 = 6.60

 

(8)(0.62) + (9)(0.25) =? 7.21

4.96 + 2.25 =? 7.21

7.21 = 7.21

Answer 2

 

5X + 14B = 6.60

 

SOLVE FOR X OR B.  Then replace x or b in the other equation.  This is substitution.  8x + 9b = 7.21

 

x = (14b + 6.60) / 5 then solve for b.  Next substitute that into the equation to get x.