# Math Help - math prroblem

1. ## math prroblem

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

2. 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 $C$ = cost of a chocolate bar.
Let $G$ = cost of a pack of bum.

Sally bought 3 chocolate bars at $C$ cents each.
. . They cost her: . $3C$ cents.
She bought 1 pack of gum at $G$ cents each.
. . This cost her: . $G$ cents.
So she spent: .3C + G[/tex] cents.
. . But we are told that she spent 175 cents.
There is one equation: . $3C + G \:=\:175$ .[1]

Jake bought two chocolate bars at $C$ cents each.
. . This cost him: .[ $2C$ cents.
He bought 4 packs of gum at $G$ cents each.
. . This cost him: . $4G$ cents.
So he spent: . $2C + 4G$ cents.
. . But we are told that he spent 200 cents.
There is another equation: . $2C + 4G \:=\:200$ .[2]

Solve the system of equations: . $\begin{array}{cccc} 3C +G & = & 175 & [1] \\ 2C + 4G & = & 200 & [2]\end{array}$

Multiply [1] by -4: . $\text{-}12C - 4G \:=\:\text{-}700$
. . . . . . .Add [2]: . . $2C + 4G \:=\:\; 200$

And we get: . $-10C \:=\:-500\quad\Rightarrow\quad\boxed{ C \,= \,50}$

Substitute into [1]: . $3(50) + G \:=\:175\quad\Rightarrow\quad\boxed{ G \,=\,25}$

Therefore: a chocolate bar costs 50¢ and a pack of gum costs 25¢.

thankyou