Help with algebraic word problems

Question

you went shopping for back to school and bought packs of pens and pencils. a pack of pencils cost 2.50 and a pack of pens cost $3. you spent a total of $35 and bought a total of 13 packs. how many packs of pencils and how many packs of pens did you buy

Answer 1

For this, you will need 2 equations:

Let x be pencils and y be pens.

The total number of packs of pencils and pens is 13. This can be expressed as an equation as follows:

X + Y = 13

The cost of pencils (X) is $2.50. The cost of pens(Y) is $3. Combined the total amount costs $35. This can be expressed as an equation as follows:

2.50X + 3Y = 35

This becomes a system of equations where, when graphed, make an intersection. This intersection is the point where X and Y are the same for both equation. To solve this algebraically, we must first have a variable by itself. In this case, let's use the first equation and isolate X:

X + Y = 13 X = 13-Y

Now that we have X, let's substitute this value in for X in the second equation and solve for Y:

2.50X + 3Y = 35

2.50(13-Y) + 3Y = 35 Distribute the 2.50 to both terms.

32.50 - 2.5Y + 3Y = 35 Add like terms.

32.50 +0.5Y = 35 Isolate the Y term on one side.

0.5Y = 2.5 Divide both sides to find Y.

Y = 5

Substitute this Y value back into the first equation to solve for X:

X = 13 - Y

X = 13 - 5

X = 8

Therefore, you would need 8 pencils and 5 pens.

To easily check this solution, substitute both values into the equations. You should have the left side of the equation equal the right side of the equation.