Mark Is Treating His Family To Ice Cream. He Buts 4 Sundaes And 3 Cones For A Total Of $26. Brian Also Buys Ice Cream For His Family. His Total Is $29

Mark is treating his family to ice cream. He buts 4 sundaes and 3 cones for a total of $26. Brian also buys ice cream for his family. His total is $29 for purchasing 2 cones and 5 sundaes.

 

Answer:

  1. Price of sundae=$5.00
  2. Price of cone=$2.00

Step-by-step explanation:

This type of problem is considered as two equation and two unknown.

Step 1: Identify the unknown

The price of each sundae and cone is unknown. We should let:

  1. sundae be equal to x
  2. cone be equal to y

Step 2: Set-up the two equations

  1. The equations will be based from the expenses of Mark and Brian.
  2. Expenses of Mark: 4 sundaes + 3 cones=$26.00
  3. Expenses of Brian: 5 sundaes + 2 cones=$29.00
  4. Incorporating Step 1, the two equations is shown below.

Equation 1: 4x + 3y = $26.00

Equation 2: 5x + 2y = $29.00

Step 3: Solve for x and y

The equations can be solved via substitution or elimination. In this problem, I will illustrate substitution.

Substitution:

Let one of the equations be in terms of x or y.

Equation 1 in terms of x:4x= 26 - 3y \\ x=\frac{26-3y}{4}

Note: Please remember that  when transposing a term the sign changes.

Use the rearranged equation 1 and substitute it to equation 2.

5 ( \frac{26-3y}{4})+2y=29\\ (\frac{5}{4})(26-3y) + 2y=29\\ \frac{65}{2} -\frac{15}{4}y +2y=29\\ -\frac{15}{4}y +2y=29-\frac{65}{2} \\ -\frac{7}{4}y=-\frac{7}{2}\\ y= 2 dollars

With a value of y in hand, then we can now compute for the value of x.

x=\frac{26-3y}{4}\\ x=\frac{26-(3)(2)}{4}\\ x=5 dollars


Therefore, the price of sundae is $5.00 and that of the cone is $2.00.



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