Jelly Shop
Write a system of equations to describe the situation below, solve using elimination,and fill in the blanks.
At a candy store, Gavin bought 2 kilograms of jelly beans and 2 kilograms of gummy worms for $32. Meanwhile, Dustin bought 2 kilograms of jelly beans and 1 kilogram of gummy worms for $25. How much does the candy cost?
A kilogram of jelly beans costs $~~~~, and a kilogram of gummy worms costs $~~~~~
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1 solution
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.
Before you can solve, you must write a system of equations. Let x = the cost of a kilogram of jelly beans, and let y = the cost of a kilogram of gummy worms.
2x + 2y = 32 2x + y = 25
Now use elimination to solve the system of equations.
-(2x + 2y = 32) → -2x – 2y = -32 2x + y = 25 → 2x + y = 25 Take the result of Step 2, y = 7, and plug it into one of the original equations, such as 2x + 2y = 32. Then find the value of x.
Since x = 9 and y = 7, the solution is (9, 7).
A kilogram of jelly beans costs $9, and a kilogram of gummy worms costs $7