Let us take costs of a piece of toast = $t, , one bagel cost=$b and a muffin cost=$m.
Larry
Two pieces of toast and a bagel cost = $1.30
2t+b=1.30 -------------equation(1)
Let us solve the equation(1) for t in terms of b, because we need to find one bagel cost.
Subtracting b from both sides we get
2t+b-b=1.30-b
2t= 1.30-b
Dividing by 2 on both sides.
2t/2= (1.30-b)/2
t= (1.30-b)/2
Curly
A bagel and a muffin cost = $2.50.
b + m = 2.50 -------------equation(2)
Solving equation for m in terms of b, we get
m= 2.50-b.
Moe
A piece of toast, two bagels, and three muffins cost = $6.95
t + 2b + 3m = 6.95 ......................equation(3).
Substituting t= (1.30-b)/2 and m= 2.50-b in equation (3)
(1.30-b)/2 + 2b + 3(2.50-b) = 6.95 .
Multiplying each term by 2 to get rid 2 from denominator of (1.30-b).
2*(1.30-b)/2 + 2*2b + 2*3(2.50-b) = 2*6.95
1.30-b + 4b + 6(2.50-b) = 13.90.
1.30 - b + 4b +15 - 6b = 13.90
Combining like terms
-3b +16.30 = 13.90
Subtracting 16.30 from both sides.
-3b +16.30-16.30 = 13.90-16.30.
-3b= -2.4
Dividing both sides by -3.
-3b/-3 = -2.4/-3
b = 0.8
Therefore, cost of one bagel = $0.80.
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