Question

Mrs. Browning bought ice cream treats for 6 children. Each child picked either a sundae or a milkshake. The sundaes cost $2 each and the milkshakes cost $5 each. If Mrs. Browning spent a total of $21, how many of each type of treat did she buy?

Answer 1

she bought 3 sundaes and 3 milkshakes

Explanation:

let's call the amount of milkshakes M.

let's call the amount of sundaes S.

you know that in total, there are 6 children.

so, you can make the following equation:

M + S = 6

if the milkshakes cost 5$ each, then the cost of the milkshakes can be expressed as 5m

if the sundaes cost 2$ each, then the cost of the sundaes can be expressed as 2S

you also know that Mrs. Browning spent 21$ in total.

so, you can make the following equation:

5m + 2S = 21

this is a system of equations.

using the first equation, you know that M = 6 - S

you can substitute M for 6 - S in the second equation

5m + 2s = 21

5(6 - s) + 2s = 21

30 - 5s + 2s = 21

30 - 3s = 21

30 = 21 + 3s

30 - 21 = 3s

9 = 3s

3 = s

now that you know how many sundaes there are, you can substitute that into the first equation:

m + s = 6

m + 3 = 6

m = 6 - 3

m = 3

Answer 2

3 milkshakes 3 sundaes

Explanation:

First write the equation.

y = total cost

x = cost of sundae

z = cost of milkshake

21=2x+5z

x+z=6 or x = 6-z

substitute in x = 6-z into the first equation

21 = 2(6-z) + 5z

21 = 12 - 2z + 5z

21 = 12 + 3z

subtract 12 from both sides

21 - 12 = 12 - 12 + 3z

9 = 3z

divide both sides by 3

3 = z

so she bought 3 milkshakes.

That means x+z = 6 and z=3 so

x+ 3 = 6, then x=3 as well, so she bought 3 sundaes.

please give thanks by clicking the heart button :)