Question

3. Mrs.Galicia bought 3 tacos and 2 sodas and paid $9.75. The next day she went back and bought 5 tacos and 1 soda and paid $12.75. (a) Write and solve a system of equations that model the problem. Show all your work. (b) How much was one soda? (c) How much was one taco?

Answer 1

(a) System of equations:
`\bold{3m + 2n = 9.75}` and
`\bold{5m + n = 12.75}`

(b) One soda costs
`\bold{\$1.5}`

(c) One taco costs
`\bold{\$2.25}`

SOLUTION:

Given, Mrs. Galicia bought 3 tacos and 2 sodas and paid
`\$9.75`.

The next day she went back and bought 5 tacos and 1 soda and paid
`\$12.75`.

Let the cost of 1 tacos be m, and cost of 1 soda be n.

Now, We have to find

(a) System of equations:

3 tacos and 2 sodas cost
`\$ 9.75 \rightarrow 3 * m+2 * n=\$ 9.75 \rightarrow 3 m+2 n=9.75 \rightarrow(1)`

5 tacos and 1 soda cost
`\$ 12.75 \rightarrow 5 * m+1 * n=\$ 12.75 \rightarrow 5 m+n=12.75 \rightarrow(2)`

System of equations are

`3m + 2n = 9.75`

`5m + n = 12.75`

Now,
`(2) \rightarrow n=12.75-5 m`

So, substitute n in (1)

`\begin{array}{l}{3 m+2(12.75-5 m)=9.75} \\\\ {3 m+25.5-10 m=9.75} \\\\ {10 m-3 m=25.5-9.75} \\\\ {7 m=15.75}\end{array}`

`\begin{array}{l}{m=2.25, \text { then, } n=12.75-5 * 2.25} \\\\ {n=12.75-11.25=1.5} \\\\ {\text {SQ, } m=2.25 \text { and } n=1.5}\end{array}`

(b) cost of one soda
`\$ 1.5`

(c) cost of one taco
`\$ 2.25`