# Solving Applied Problems: Two Equations?

problem 1

The St.mark's Community bbq served 250 dinners. A child's plate cost \$3.50 and an adult's plate cost \$7.00. A total of \$1347.50 was collected. How many of each type of plate was served?

Relevance

We have two totals:

250 total dinners served.

\$1347.50 collected.

Let

x=number of child's plates served

Then we can set up 2 equations with 2 unknowns and solve:

x+y=250

3.50x+7.00y=1347.50

Multiplying the first equation by -3.5 yields

-3.50x-3.50y= -875

3.50x+7.00y=1347.50

3.50y=472.50

so y=135

Recall that x+y=250

so x+135=250

and x=115

So there were 115 child plates and 135 adult plates served.

• Call x the number of child's plates sold and y the number of adult's plates sold. The total number of dinners sold is 250, so:

x + y = 250

The total cost is 1347.50, so:

(3.50)x + (7.00)y = 1347.50

Solving by substitution, the first equation can be written:

x = 250 - y

Now plug into the second equation for x

(3.50)(250-y) + (7.00)y = 1347.50

875 - (3.50)y + (7.00)y = 1347.50

(3.50)y = 472.5

so the rest (250-135) must be children's plates x = 115

Checking 115(3.50) + 135(7) = 1347.50

• you have 2 equations here. If x is the sort of 30 2d commercials and y the sort of 60 2d commercials, x + y is 12 and 30*x + 60*y = 10*60, or six hundred. So i might propose substitution. Y = 12 - x. 30 * x + 720 - 60*x = six hundred. 30 * x = a hundred and twenty. X = 4, and for this reason y = 8. you may verify this: 4 * 30 + 8 * 60 = six hundred seconds, or 10 minutes.

• you can establish 2 equations with the above data.

lets say x= the number of children in attendance

and y=the number of adults in attendance

so x+y=250 people

we also know that

(\$7*y)+(\$3.5*x)=\$1347.50

solve one equation for the variable of your choice

x+y=250

x=250-y

substitute the value of x for this answer in your other equation so

3.5(250-y)+7y=1347.5

multiply 3.5 through

875-3.5y-7y=1347.5

combine like terms and move the 875 to the other side

3.5y=472.5

solve for y

y=135 the number of adults in attendance

use this to solve for x

x+135=250

x=115 the number of children in attendance

• Suppose x= number of child's plates were served

y=number of adult's plates were served

So: 3.5x+7y= 1347.5

x + y= 250

<=> 3.5x+7y= 1347.5 

3.5x+3.5y= 875 (250*3.5) 

 -  : 3.5y = 472.5

=>

x=115

y=135