Question

Marina volunteers at the salvation army. she has been tasked with buying non-perishable items for families that were displaced by a recent flood. she finds a company willing to sell her cans of food at a discounted price. in the system below x represents the number of small cans she purchased and y represents the number of large cans she purchased.

2.25x+4.75y=714.75
x+y=181

Part A: How many cans did she purchase?
Part B: What was the total amount marina spent on the purchase?
Part C: How many small cans did marina purchase?
Part D: How many large cans did marina purchase?
Part E: How much does a small can cost?
Part F: How much does a large can cost?

Answer 1

part A:

if she bought X small cans and y large cans,then she bought X+Y cans.since X=Y=181,then she bought 181 cans

part B:

since the second equation tell us how many cans she bought ,the first equation must be telling us how much she spent.since the first equation is 2.25x+4.75y=714.25,then the total amount she spent is $714.75.

part C :

solving the second equation for y by subtracting x on both sides gives y=181-x.substitute this into the first equation and solve for x

2.25x+4.75y=714.75

2.25x +4.75 (181-c)=714.75 substitute

2.25x+859.75-4.75=714.75 distribute

859.75 - 2.5x =714.75 combine like terms

-2.5x= -145 subtract 859.75 on both sides

x = 58 divide both sides by -2.5

marina then purchased 58 small cans

part D :

since x = 58 and y = 181-x then y= 181 - 58= 123. marina then purchased 123 large cans .

part E:

the first equation of 2.25x + 4.75y = 714.75 represented the total amount she spent .since x is being multiplied by 2.25,then each small can cost $2.25.

part F :

since y in the first equation is being multiplied by 4.75,then each large can costs $4.75.

Answer 2

See below for each answer

Explanation:

What we have to do here is solve the equation system:

2.25x+4.75y=714.75 [equaiton 1]

x+y=181 [equaiton 2]

For this, lets take equation 2 and try to get the value of x as a function of y. We do so by subtracting x in both sides:

x+y - y=181 - y

x = 181 -y [eqaution 1*]

Now, we can replace this value of x in equation 1, so we get an equation with only one unknown variable y:

2.25x+4.75y=714.75

2.25(181-y) + 4.75y = 407.25 - 2.25y + 4.75y = 407.25 + 2.5y = 714.75

Now, subtract 407.25 in both sides:

407.25 + 2.5y - 407.25 = 714.75 - 407.25

2.5 y = 307.5

Dividing both sides by 2.5:

2.5y/2.5 = 307.5/2.5

y = 123

Now, we can find x replacing y=123 in equation 1*:

x = 181 - 123 = 58

x = 58

So, we can answer questions A, B ans C:

A) to know how many she purchased we have to sum small cans (58) and large cans (y), which is given by equation 1: 181 cans.

B) Then equation 2 shows the total expenditure in cans, summing each can number by its respective price. The total expenditure is 714.75

C) The number of small cans is given by x: 58

D) The number of large cans is given by y: 123

E) The cost of small cans is given by the price, the number that multiplies the x in the expenditure equation (Equation 1): 2.25 costs a small can.

F) The cost of large cans is given by its price, the number that multiplies the y in the expenditure equation (Equation 2): 4.75 is the cost of large cans.