Question

Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. Determine a system of equations that represents the given the situation. Let x be cost per pound of apples and let y be the cost per pound of bananas. Which equation represents the amount of money Lydia spent of apples and bananas? Which equation represents the amount of money Ari spent on apples and bananas?

Answer 1

We have,

Lydia purchases 5 pounds of apples (x) + 3 pounds of bananas (y) at $8.50

and, Ari purchases 3 pounds of apples (x) + 2 pounds of bananas (y) at $5.25

So, we have the following equations:-

Lydia's purchase = 5x + 3y = 8.50 (eqn 1)

Ari's purchase = 3x + 2y = 5.25 (eqn 2)

Now to find the values of x and y, we use simulation to find the value of one of the variables;

Step 1  : $\left \{{{[5x + 3y = 8.50] * (-2)}\atop{[2x + 3y = 5.25] * (3)}} \right.$    

[∵ LCM of 2 and 3 = 6; hence (-2) and (-3) to cancel one common variable from the two eqns.]

Step 2 : $\left \{ {{-10x - 6y = -17} \atop {9x + 6y = 15.75}} \right.$

Step 3 :  $\left \{ {{-10x = -17} \atop {9x = 15.75}} \right.$

⇒ $-x = -1.25$

⇒ $x = 1.25$

Thus, cost per pound of apples = $1.25

On substituting the value of x in eqn 1, we get;

$(5 * 1.25) + 3y = 8.50$

⇒ $3y = 8.50 - 6.25$

⇒ $y = \frac{2.25}{3} = 0.75$

Hence, cost per pound of bananas = $0.75

Ans) The following set of equations represent the given scenario;

Lydia's purchase = 5x + 3y = 8.50 (eqn 1)

Ari's purchase = 3x + 2y = 5.25 (eqn 2)

Answer 2

Given : Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50.

Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25.

To Find : Determine a system of equations that represents the given the situation

Solution:

x be cost per pound of apples

y be the cost per pound of bananas.

Lydia

5 pounds of apples and 3 pounds of bananas  = $8.50

=> 5x  + 3y  = 8.5

Ari

3 pounds of apples and 2 pounds of bananas for a total of $5.25.

=> 3x  + 2y  = 5.25

5x  + 3y  = 8.5    Eq1

3x  + 2y  = 5.25  Eq2

=> 2 * Eq1 - 3 * Eq2

=> x  = 17 - 15.75

=> x = 1.25

3x  + 2y  = 5.25

=> 3.75 + 2y = 5.25

=> 2y = 1.5

=> y = 0.75

cost per pound of apples   = 1.25 $

cost per pound of bananas.  = 0.75 $

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