Andre wants to purchase some onions and tomatoes to make tomato soup. the recipe states that four times the number of tomatoes, , plus five times the number of onions, x, should produce 56 bowls of tomato soup. a different recipe states that two times the number of tomatoes used minus the number of onions used should produce 21 bowls of tomato soup. what is the resulting recipe for the number or tomatoes and onions used in the soup when andre adds the two recipes together?

in the resulting recipe, 2 onions were used and 11.5 tomatoes were used.

Step-by-step explanation:

Let x represent the number of onions used.

Let y represent the number of tomatoes used.

The recipe states that four times the number of tomatoes, , plus five times the number of onions should produce 56 bowls of tomato soup. This means that

5x + 4y = 56 - - - - - - - - - - - - -1

A different recipe states that two times the number of tomatoes used minus the number of onions used should produce 21 bowls of tomato soup. This means that

2y - x = 21

-x + 2y = 21 - - - - - - - - - - - - - - 2

Multiplying equation 1 by 1 and equation 2 by 5, it becomes

5x + 4y = 56

-5x + 10y = 105

Since the two recipes were added together, we would add both equations. It becomes

14y = 161

y = 161/14 =11.5

Substituting y = 11.5 into equation 1, it becomes

-x + 2 × 11.5 = 21

-x + 23 = 21

-x = 21 - 23 = -2

x = 2