Question

Using a graph, determine the price per bag of sand (X) and the price per bag of pea gravel (Y) based on the given information. You bought four bags of sand and three bags of pea gravel for $24, and in a second purchase, you bought two bags of sand for $6.

a) X = $3, Y = $6
b) X = $4, Y = $5
c) X = $2, Y = $7
d) X = $5, Y = $4

Answer 1

By solving two equations representing purchases of bags of sand and pea gravel, we find the price per bag of sand (X) to be $3 and the price per bag of pea gravel (Y) to be $4.

Step-by-step explanation:

The question presents two linear equations based on purchases made. From the given information, the two equations representative of the purchases are:

1) 4X + 3Y = $24 (First purchase of sand and pea gravel)

2) 2X = $6 (Second purchase of just sand).

Solving the second equation directly gives the price of one bag of sand:

X = $6 / 2

X = $3

We substitute the value of X into the first equation to find Y:

4($3) + 3Y = $24

$12 + 3Y = $24

3Y = $24 - $12

3Y = $12

Y = $12 / 3

Y = $4

Therefore, the price per bag of sand (X) is $3, and the price per bag of pea gravel (Y) is $4, which corresponds to option a).