store a sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. store b sells raspberries…

store a sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. store b sells raspberries for $6.50 per pint and blackberries for $8.00 per pint. a certain purchase of raspberries and blackberries would cost $37.00 at store a or $66.00 at store b. how many pints of blackberries are in this purchase? a. 4 b. 5 c. 8 d. 12

store a sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. store b sells raspberries for $6.50 per pint and blackberries for $8.00 per pint. a certain purchase of raspberries and blackberries would cost $37.00 at store a or $66.00 at store b. how many pints of blackberries are in this purchase? a. 4 b. 5 c. 8 d. 12

Answer

Explanation:

Step1: Let the number of pints of black - berries be $x$.

Let the number of pints of raspberries be $y$. We know that the cost equation for Store A is $6.5y + 3x=37$. The cost equation for Store B is $5y+8x = 66$.

Step2: Multiply the first equation by 5 and the second equation by 6.5 to eliminate $y$.

The first equation $6.5y + 3x=37$ multiplied by 5 gives $32.5y+15x = 185$. The second equation $5y + 8x=66$ multiplied by 6.5 gives $32.5y+52x=429$.

Step3: Subtract the first new - equation from the second new - equation.

$(32.5y + 52x)-(32.5y+15x)=429 - 185$. $32.5y+52x - 32.5y - 15x=244$. $37x=244$. $x = 8$.

Answer:

C. 8