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

Question

andrey2020 [161]

3 years ago

8

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. this system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas. 5x 3y = 8.5 3x 2y = 5.25 if you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination? complete the multiplication and add the equations. what is the result? what is the price per pound of apples? $ what is the price per pound of bananas? $

Mathematics

2 answers:

gavmur [86] · Answer 1 · 2021-12-05T12:08:34+03:00

Answer: The price per pound of apples is $ 1.25 and the price per pound of bananas is $ 0.75.

Step-by-step explanation: Given that lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50 whereas Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25.

We are to find the price per pound of apples and bananas.

The cost per pound of apples is represented by x dollars and the cost per pound of bananas is represented by y dollars.

Then, according to the given information, the system of equations describing the situation is as follows:

$5x+3y=8.50~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x+2y=5.25~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Multiplying equation (i) by 2, we have

$2(5x+3y)=2\times 8.50\\\\\Rightarrow 10x+6y=17~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

and multiplying equation (ii) by 3, we have

$3(3x+2y)=3\times 5.25\\\\\Rightarrow 9x+6y=15.75~~~~~~~~~~~~~~~~~~~~~~~~(iv)$

To eliminate y, we subtract equation (iv) from equation (iii) and we arrive at

$(10x+6y)-(9x+6y)=17-15.75\\\\\Rightarrow x=1.25.$

From equation (i), we get

$5\times 1.25+3y=8.50\\\\\Rightarrow 6.25+3y=8.50\\\\\Rightarrow 3y=2.25\\\\\Rightarrow y=0.75.$

Thus, the price per pound of apples is $ 1.25 and the price per pound of bananas is $ 0.75.

Monica [59] · Answer 2 · 2021-12-05T13:35:08+03:00

5x + 3y= 8.50
3x + 2y= 5.25

Lydia is the first equation. She bought 5 pounds of apples which is x and bought 3 pounds of bananas which is y. Basically, remember each banana and apple weighs a price per pound. We don't know the price so we just put an x. This is the same for the second equation
Hope it helps