Question

William buys two bags of peaches and three bags of apricots for $17. Sylvia buys four bags of peaches and two bags of apricots for $22 from the same store. What is the cost of one bag of peaches? $3 $4 $5 $7

Answer 1

$4 dollars. My process was first, creating the matrix.

17= 2p + 3a p represents peaches and a for apricot
22= 4p + 2a

Answer 2

Answer: The correct option is (B) $4.

Step-by-step explanation: Given that William buys two bags of peaches and three bags of apricots for $17 and Sylvia buys four bags of peaches and two bags of apricots for $22 from the same store.

We are to find the cost of one bag of peaches.

Let $x and $y be the cost of one bag of peaches and one bag of apricots respectively.

Then, according to the given information, we have

`2x+3y=17~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\4x+2y=22~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Multiplying equation (i) by 2, we have

`2(2x+3y)=2* 17\\\\\Rightarrow 4x+6y=34~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Subtracting equation (ii) from equation (iii), we get

`(4x+6y)-(4x+2y)=34-22\\\\\Rightarrow 4y=12\\\\\Rightarrow y=3.`

Substituting the value of y in equation (i), we get

`2x+3y=17\\\\\Rightarrow 2x+3*3=17\\\\\Rightarrow 2x+9=17\\\\\Rightarrow 2x=8\\\\\Rightarrow x=4.`

Thus, the cost of one bag of peaches is $4.

Option (B) is CORRECT.