at an ice cream store, ice cream cones cost $2.00 and sundaes cost $3.50. one day, the receipts for a total of 139 cones and sundaes were $408.50.

Question

how many cones and sundaes were sold? solve the equations by using the substitution method.

Answer 1

To solve this problem you just create two equations each with two variables. One of the equations will be based on the number of items sold and the other equation will be based on the prices.

 

If x = the number of cones sold and y = the number of sundaes sold, then your first equation is simply x + y = 139 since the total number of items sold was 139.  

 

The other equation involves price.  The revenue from cones is simply 2x since each cone sold for $2.  The revenue from sundaes is 3.5y.  Therefore, the second equation of the system is 2x + 3.5y = 408.5

 

If the desired method is substitution, solve the first equation for either x or y and substitute into the second equation.  

 

Given this setup, give it a shot. Comment if any questions remain...

 

Answer 2

let;

 

C = number of ice cream cones sold

S = number of sundaes sold

 

total of 139 cones and sundaes sold were $408.50.

 

Write an equation representing the total number of cones and sundaes.

 

C + S = 139

 

Write an equation representing the total cost of all the cones and sundaes.

 

2C + 3.5S = 408.5

 

Now there are two equations. rearrange the first equation using algebra to equal one of the unknown variables.

 

C + S = 139

C = 139 - S

 

Now substitute (139 - S) into the second equation for C.

 

2(139 - S) + 3.5S = 408.5

 

Solve for S, the number of sundaes sold

 

278 - 2S + 3.5S = 408.5

1.5S = 408.5 - 278

1.5S = 103.5

S = 103.5/1.5

S = 87

 

If 87 sundaes were sold out of a total 139 cones + sundaes, then;

 

87 + C = 139

C = 139 - 87

C = 52