Question

Drew bought 3 pounds of beans and 2 pounds of peppers for $7.05. Last week he bought 4 pounds of beans and 3 pounds of peppers for $9.83. The price for both items stayed the same both weeks what is the cost per pound

Answer 1

Cost of each pound of beans is #1.49 and pepper is $1.29

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

Answer 2

A pound of beans cost $1.49 and a pound of pepper costs $1.29.

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.