please help me solve this
sally bought three cholate bars and a pack of gum and paid $1.75. Jake bought two cholate bars and four packs of gum and paid $2.00. Find the cost of a chocolate bar and the cost of a pack of gum
Hello, lizard4!
This is a very basic problem with a system of equations.
Assuming you're new at this, I'll baby-step through it.
Sally bought three chocolate bars and a pack of gum and paid $1.75.
Jake bought two chocolate bars and four packs of gum and paid $2.00.
Find the cost of a chocolate bar and the cost of a pack of gum
Let $\displaystyle C$ = cost of a chocolate bar.
Let $\displaystyle G$ = cost of a pack of bum.
Sally bought 3 chocolate bars at $\displaystyle C$ cents each.
. . They cost her: .$\displaystyle 3C$ cents.
She bought 1 pack of gum at $\displaystyle G$ cents each.
. . This cost her: .$\displaystyle G$ cents.
So she spent: .3C + G[/tex] cents.
. . But we are told that she spent 175 cents.
There is one equation: .$\displaystyle 3C + G \:=\:175$ .[1]
Jake bought two chocolate bars at $\displaystyle C$ cents each.
. . This cost him: .[$\displaystyle 2C$ cents.
He bought 4 packs of gum at $\displaystyle G$ cents each.
. . This cost him: .$\displaystyle 4G$ cents.
So he spent: .$\displaystyle 2C + 4G$ cents.
. . But we are told that he spent 200 cents.
There is another equation: .$\displaystyle 2C + 4G \:=\:200$ .[2]
Solve the system of equations: .$\displaystyle \begin{array}{cccc} 3C +G & = & 175 & [1] \\ 2C + 4G & = & 200 & [2]\end{array}$
Multiply [1] by -4: .$\displaystyle \text{-}12C - 4G \:=\:\text{-}700$
. . . . . . .Add [2]: . . $\displaystyle 2C + 4G \:=\:\; 200$
And we get: .$\displaystyle -10C \:=\:-500\quad\Rightarrow\quad\boxed{ C \,= \,50}$
Substitute into [1]: .$\displaystyle 3(50) + G \:=\:175\quad\Rightarrow\quad\boxed{ G \,=\,25}$
Therefore: a chocolate bar costs 50¢ and a pack of gum costs 25¢.