Answer:
A pound of beans cost $1.49 and a pound of pepper costs $1.29.
Step-by-step explanation:
Let the cost per pound of beans=b
Let the cost per pound of pepper=p
Drew bought 3 pounds of beans and 2 pounds of peppers for $7.05.
That gives his cost:
3b+2p=$7.05
Similarly, he bought 4 pounds of beans and 3 pounds of peppers for $9.83.
His cost in this case is represented by:
4b+3p=$9.83
We solve the two equations we have derived simultaneously.
3b+2p=$7.05
4b+3p=$9.83
To eliminate p, multiply the first equation by 3 and the second equation by 2.
9b+6p=21.15
8b+6p=19.66
Next we Subtract
b=1.49
Substitute b=1.49 into any of the equations to obtain p.
3b+2p=$7.05
3(1.49)+2p=7.05
4.47+2p=7.05
2p=7.05-4.47
2p=2.58
p=1.29
Since b=$1.49, b=$1.29
Therefore a pound of beans cost $1.49 and a pound of pepper costs $1.29.
Answer:
Cost of each pound of beans is #1.49 and pepper is $1.29
Step-by-step explanation:
Let the cost of each pound of beans represent x and the cost of each pound of pepper represent y.
Since the total cost of 3 pounds of beans and 2 pounds of pepper is $7.05,we derive its first equation:
3X+2Y= 7.05
AND
The other week he bought 4 pounds of beans and 3 pounds of pepper for a combined cost of $9.83 without a change in price in both items during the past few weeks.
Second equation will be:
4X+3Y= 9.83.
Here we have a simultaneous equation and we are going to use the substitution method to get X and Y.
From the first equation, 3X+2Y=7.05
X= (7.05-2Y)/3.
Apply the above in the second equation(4X+3Y= 9.83.)
4×{(7.05-2Y)/3}
(28.2-8y+9y)/3=9.83
Y=1.29
Replace Y=1.29 in equation 1 and we have
3x+(2×1.29)=7.05
X=1.49
Therefore the prices of each pound of beans and that of pepper is $1.49 and $1.29 respectively
