IXL - Solve a system of equations using any method: word problems (Algebra 2 practice)

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Zeke and his little sister are saving up money to buy a joint birthday present for their mother. Zeke already has $16 saved and plans to save $17 per week from his allowance. His sister has $22 saved so far and will save $14 per week from hers. The two siblings will soon have saved the same amount towards their mother's gift. How much will each one have saved? How long will that take?

Zeke and his sister will each have saved $ in weeks.

ref_doc_title.

Learn with an example

question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

The drama club is selling gift baskets to raise money for new costumes. During the fall play, they sold a combined 17 regular gift baskets and 1 deluxe gift basket, earning a total of $316. During the spring musical, they sold 12 regular gift baskets and 1 deluxe gift basket, earning a total of $236. How much are they charging for the different sized gift baskets?

The drama club is charging $ for a regular gift basket and $ for a deluxe gift basket.

key idea

To solve using elimination, follow these four steps:

Step 1: Make sure the equations have opposite x terms or opposite y terms.

Step 2: Add to eliminate one variable and solve for the other.

Step 3: Plug the result of Step 2 into one of the original equations and solve.

Step 4: State the solution.

solution

Before you can solve, you must write a system of equations. Let x represent the amount charged for a regular gift basket, and let y represent the amount charged for a deluxe gift basket.

17x + y = 316

12x + y = 236

Now use any method to solve the system of equations, such as elimination.

Step 1: Make sure the equations have opposite x terms or opposite y terms.

Currently, neither the x terms (17x and 12x) nor the y terms (y and y) are opposites. Use multiplication to rewrite the equations with either opposite x terms or opposite y terms. One good approach is to multiply the first equation by ^–1.

^–(17x + y = 316)

→

^–17x − y = ^–316

12x + y = 236

→

12x + y = 236

Now the y terms (^–y and y) are opposites.

Step 2: Add to eliminate one variable and solve for the other.

Add to eliminate the y terms, and then solve for x.

Add to eliminate the y terms
	^–17x	−	y	=	^–316
+ (	12x	+	y	=	236	)


	^–5x	+	0y	=	^–80	Add to eliminate the y terms

Simplify
			^–5x	=	^–80	Simplify

Divide both sides by ^–5
			x	=	16	Divide both sides by ^–5

Step 3: Plug the result of Step 2 into one of the original equations and solve.

Take the result of Step 2, x = 16, and plug it into one of the original equations, such as 17x + y = 316. Then find the value of y.

17x + y

316

Plug in x = 16

17(16) + y

316

Plug in x = 16

Multiply

272 + y

316

Multiply

Subtract 272 from both sides

Step 4: State the solution.

Since x = 16 and y = 44, the solution is (16, 44).

The drama club is charging $16 for a regular gift basket and $44 for a deluxe gift basket.

Looking for more? Try these:

Lesson: Systems of equations

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

E.10Solve a system of equations using any method

E.7Solve a system of equations using substitution: word problems

E.9Solve a system of equations using elimination: word problems

Lesson: Systems of equations

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!