Solving systems of equations word problems worksheet for all problems, define variables, write the system of equations and solve variables.

Question

The frosty Ice-cream shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156.

Answer 1

Hello, Silvio,

Set S=the number of sundaes, and B=the number of banana splits. We are told we have 5 more sundaes than banana split (1st row). We also know the total value of sundaes is 2S and the total value of banana splits is 3B, and that their sum for that hot summer day is $156 (line 2). Substitute the value of S from line 1 into the equation in line 2 and then solve for B. Once you have B, use that value in the line 1 equation to find S.

Use the values of B and S to see if they satisfy the equation for the day's total sales value. If they do, then we probably have a correct answer.

Bob

Answer 2

The variables are the number of items sold for sundaes and banana splits.

Let's say the number of sundaes = s

and the number of banana splits = b

We know the number of sundaes sold is 8 more than the number of banana splits, so s= b+8

We also know that the total amount earned in the day = $156 and sundaes are $2 and banana splits $3

To write the algebraic equation to represent the number of items sold, multiply the cost by the number of items and set it equal to the total earned.

$2(s) + $3(b) = $156

Since we know s = b + 8, the second part of the equation can be substituted for s to solve for b

$2(b + 8) + $3(b) = $156

Distribute following the order of operations

$2b + $16 + $3b = $156

Simplify

$5b + $16 = $156

Subtract $16 from both sides to get all the variables on one side of the equation

$5b + $16 - $16 = $156 - $16

$5b = $140

Divide both sides of the equation by $5 to isolate the variable

$5b\$5 = $140/$5

This gives us the value of b = 28

Now we can solve for s by putting the value of b into our equation for the number of s

s = b + 8

s = 28 + 8

s = 36

Now that we know s = 36 and b = 28 we can use the values to check our answer

$2(s) + $3(b) = $156

$2(36) = $3(28) = $156

$72 + $84 = $156

$156 = $156

Hope this helps!