SOLVE WORD PROBLEM

Question

On Monday, Harold picked up two donuts and four large coffees for the office staff. He paid $5.10. On Tuesday, Melinda picked up six donuts and three large coffees for the office staff. She paid $6.39. What is the cost of one donut? What is the cost of one large coffee?

Answer 1

Suppose the cost of each donuts is $X, and the cost of each large coffee is $Y. 

 

We can set up the system equation for it:

 

2 X + 4 Y = $5.10----(Equation 1)

6 X + 3 Y = $6.39----(Equation 2)

 

 

Equation 1 multiply by 3: 6 X + 12 Y = $15.30

Subtract Equation 2: 9 Y = $8.91

Divide by 9: Y = $0.99 (Each large coffee)

 

Substitute Y = $0.99 into Equation 1:

2 X + 4 Y = $5.10

2 X + 4 ($0.99) = $5.10

2 X + $3.96 = $5.10

2 X = $1.14

X = $0.57 (Each donut)

 

The cost of one donut is $0.57, and the cost of one large coffee is $0.99.

 

 

Answer 2

let x = cost of one donut; and let y = cost of one large coffee;  then

 

               2x + 4y = 5.10; and ---> 2x + 4y = 5.10

 

               6x + 3y = 6.39 ---------> 2x + y = 2.13

 

subtracting the bottom equation from the top equation ---> 3y = 2.97 ---> y = $0.99

 

and, then, from:  2x + 4y = 5.10 --->  x + 2y = 2.55 ---> x + 2(0.99) = 2.55 ---> x + 1.98 = 2.55 ---> x = $0.57

Answer 3

let x = the cost of donuts

y = the cost of large coffees

 

2x + 4y = 5.10

6x + 3y = 6.39

 

We can use the Elimination Method. Let's multiply both sides of the first equation by 3

 

  6x + 12y = 15.30

-(6x + 3y = 6.39)

 

9y = 8.91

y = 0.99

 

A large coffee costs 99 cents

 

2x + 4y = 5.10

2x + 4(0.99) = 5.10

2x + 3.96 = 5.10

2x = 1.14

x = 0.57

 

One donut costs 57 cents